Frank solutions for माठेमटिक्स पार्ट १ [इंग्रजी] इयत्ता १० आईसीएसई chapter 1 - Rational and Irrational Numbers [Latest edition]

State if the following fraction has a terminating decimal

`(3)/(5)`

State if the following fraction has a terminating decimal

`(5)/(7)`

State if the following fraction has a terminating decimal

`(25)/(49)`

State if the following fraction has a terminating decimal

`(37)/(40)`

State if the following fraction has a terminating decimal

`(57)/(64)`

State if the following fraction has a terminating decimal.

`(59)/(75)`

State if the following fraction has a terminating decimal.

`(89)/(125)`

State if the following fraction has a terminating decimal.

`(125)/(213)`

State if the following fraction has a terminating decimal.

`(147)/(160)`

Express the following decimal as a rational number.

0.93

Express the following decimal as a rational number.

4.56

Express the following decimal as a rational number.

0.614

Express the following decimal as a rational number.

21.025

Convert the following fraction into a decimal :

`(3)/(5)`

Convert the following fraction into a decimal :

`(8)/(11)`

Convert the following fraction into a decimal :

`(-2)/(7)`

Convert the following fraction into a decimal :

`(12)/(21)`

Convert the following fraction to a decimal:

`(13)/(25)`

Convert the following fraction into a decimal :

`(2)/(3)`

Express the following decimal as a rational number.

0.7

Express the following decimal as a rational number.

0.35

Express the following decimal as a rational number.

0.89

Express the following decimal as a rational number.

0.057

Express the following decimal as a rational number.

0.763

Express the following decimal as a rational number.

2.67

Express the following decimal as a rational number.

4.6724

Express the following decimal as a rational number.

0.017

Express the following decimal as a rational number.

17.027

Insert a rational number between:

`(2)/(5) and (3)/(4)`

Insert a rational number between:

`(3)/(4) and (5)/(7)`

Insert a rational number between:

`(4)/(3) and (7)/(5)`

Insert a rational number between:

`(5)/(9) and (6)/(7)`

Insert a rational number between:

3 and 4

Insert a rational number between:

7.6 and 7.7

Insert a rational number between:

8 and 8.04

Insert a rational number between:

101 and 102

Insert three rational numbers between:

0 and 1

Insert three rational number between:

6 and 7

Insert three rational number between:

-3 and 3

Insert three rational number between:

-5 and -4

Insert five rational number between:

`(2)/(5) and (2)/(3)`

Insert five rational number between:

`-(3)/(4) and -(2)/(5)`

Find the greatest and the smallest rational number among the following.

`(6)/(7),(9)/(14) and (23)/(28)`

Find the greatest and the smallest rational number among the following.

`(-2)/(3) , (-7)/(9) and (-5)/(6)`

Arrange the following rational numbers in ascending order.

`(4)/(5),(6)/(7) and (7)/(10)`

Arrange the following rational numbers in ascending order.

`(-7)/(12), (-3)/(10) and (-2)/(5)`

Arrange the following rational numbers in ascending order.

`(10)/(9),(13)/(12) and (19)/(18)`

Arrange the following rational numbers in ascending order.

`(7)/(4), (-6)/(5) and (-5)/(2)`

Arrange the following rational numbers in descending order.

`(7)/(13),(8)/(15), and (3)/(5)`

Arrange the following rational numbers in descending order.

`(4)/(3), (-14)/(5) and (17)/(15)`

Arrange the following rational numbers in descending order.

`(-7)/(10), (-8)/(15) and (-11)/(30)`

Arrange the following rational numbers in descending order.

`(-3)/(8),(2)/(5) and (-1)/(3)`

Find the value of:

2.65 + 1.25

Find the value of:

1. 32 - 0.91

Find the value of:

2.12 - 0.45

Find the value of:

1.35 + 1.5

State whether the following number is rational or irrational

`(3 + sqrt(3))^2`

State whether the following number is rational or irrational

`(5 - sqrt(5))^2`

State whether the following number is rational or irrational

`(2 + sqrt(2))(2 - sqrt(2))`

State if the following is a surd. Give reasons.

`root(3)(-27)`

State whether the following number is rational or irrational

`((sqrt5)/(3sqrt(2)))^2`

Check whether the square of the following is rational or irrational:

`3sqrt(2)`

Check whether the square of the following is rational or irrational:

`3 + sqrt(2)`

Check whether the square of the following is rational or irrational:

`(3sqrt(2))/(2)`

Check whether the square of the following is rational or irrational:

`sqrt(2) + sqrt(3)`

Show that `sqrt(5)` is an irrational numbers. [Use division method]

Without using division method show that `sqrt(7)` is an irrational numbers.

Write a pair of irrational numbers whose sum is irrational.

Write a pair of irrational numbers whose sum is rational.

Write a pair of irrational numbers whose difference is irrational.

Write a pair of irrational numbers whose difference is rational.

Write a pair of irrational numbers whose product is irrational.

Write a pair of irrational numbers whose product is rational.

Compare the following:

`root(4)(12) and root(3)(15)`

Compare the following:

`root(3)(48) and sqrt(36)`

Write the following in ascending order:

`2sqrt(5), sqrt(3) and 5sqrt(2)`

Write the following in ascending order:

`2root(3)(3), 4root(3)(3) and 3root(3)(3)`

Write the following in ascending order:

`5sqrt(7), 7sqrt(5) and 6sqrt(2)`

Write the following in ascending order:

`7root(3)(5), 6root(3)(4) and 5root(3)(6)`

Write the following in descending order:

`sqrt(2), root(3)(5) and root(4)(10)`

Write the following in descending order:

`5sqrt(3), sqrt(15) and 3sqrt(5)`

Write the following in descending order:

`sqrt(6), root(3)(8) and root(4)(3)`

Insert two irrational numbers between 3 and 4.

Insert five irrational number's between `2sqrt(3) and 3sqrt(5)`.

Write two rational numbers between `sqrt(3) and sqrt(7)`

Write four rational numbers between `sqrt(2) and sqrt(3)`

State if the following is a surd. Give reasons.

`sqrt(150)`

State if the following is a surd. Give reasons.

`root(3)(4)`

State if the following is a surd. Give reasons.

`root(3)(50). root(3)(20)`

State if the following is a surd. Give reasons.

`sqrt(2 + sqrt(3)`

State if the following is a surd. Give reasons.

`root(12)(8). ÷ root(6)(6)`

Represent the number `sqrt(7)` on the number line.

Simplify by rationalising the denominator in the following.

`(3sqrt(2))/sqrt(5)`

Simplify by rationalising the denominator in the following.

`(1)/(5 + sqrt(2))`

Simplify by rationalising the denominator in the following.

`(1)/(sqrt(3) + sqrt(2))`

Simplify by rationalising the denominator in the following.

`(2)/(3 + sqrt(7)`

Simplify by rationalising the denominator in the following.

`(5)/(sqrt(7) - sqrt(2))`

Simplify by rationalising the denominator in the following.

`(42)/(2sqrt(3) + 3sqrt(2)`

Simplify by rationalising the denominator in the following.

`(sqrt(3) + 1)/(sqrt(3) - 1)`

Simplify by rationalising the denominator in the following.

`(sqrt(5) - sqrt(7))/sqrt(3)`

Simplify by rationalising the denominator in the following.

`(3 - sqrt(3))/(2 + sqrt(2)`

Simplify by rationalising the denominator in the following.

`(5 + sqrt(6))/(5 - sqrt(6)`

Simplify by rationalising the denominator in the following.

`(4 + sqrt(8))/(4 - sqrt(8)`

Simplify by rationalising the denominator in the following.

`(sqrt(15) + 3)/(sqrt(15) - 3)`

Simplify by rationalising the denominator in the following.

`(sqrt(7) - sqrt(5))/(sqrt(7) + sqrt(5)`

Simplify by rationalising the denominator in the following.

`(3sqrt(5) + sqrt(7))/(3sqrt(5) - sqrt(7)`

Simplify by rationalising the denominator in the following.

`(2sqrt(3) - sqrt(6))/(2sqrt(3) + sqrt(6)`

Simplify by rationalising the denominator in the following.

`(5sqrt(3) - sqrt(15))/(5sqrt(3) + sqrt(15)`

Simplify by rationalising the denominator in the following.

`(2sqrt(6) - sqrt(5))/(3sqrt(5) - 2sqrt(6)`

Simplify by rationalising the denominator in the following.

`(7sqrt(3) -  5sqrt(2))/(sqrt(48) + sqrt(18)`

Simplify by rationalising the denominator in the following.

`(sqrt(12) + sqrt(18))/(sqrt(75) - sqrt(50)`

Simplify the following

`(3)/(5 - sqrt(3)) + (2)/(5 + sqrt(3)`

Simplify the following

`(4 + sqrt(5))/(4 - sqrt(5)) + (4 - sqrt(5))/(4 + sqrt(5)`

Simplify the following

`(sqrt(5) - 2)/(sqrt(5) + 2) - (sqrt(5) + 2)/(sqrt(5) - 2)`

Simplify the following

`(sqrt(7) - sqrt(3))/(sqrt(7) + sqrt(3)) - (sqrt(7) + sqrt(3))/(sqrt(7) - sqrt(3)`

Simplify the following

`(sqrt(5) + sqrt(3))/(sqrt(5) - sqrt(3)) + (sqrt(5) - sqrt(3))/(sqrt(5) + sqrt(3)`

Simplify the following :

`sqrt(6)/(sqrt(2) + sqrt(3)) + (3sqrt(2))/(sqrt(6) + sqrt(3)) - (4sqrt(3))/(sqrt(6) + sqrt(2)`

Simplify the following :

`(3sqrt(2))/(sqrt(6) - sqrt(3)) - (4sqrt(3))/(sqrt(6) - sqrt(2)) + (2sqrt(3))/(sqrt(6) + 2)`

Simplify the following :

`(6)/(2sqrt(3) - sqrt(6)) + sqrt(6)/(sqrt(3) + sqrt(2)) - (4sqrt(3))/(sqrt(6) - sqrt(2)`

Simplify the following :

`(7sqrt(3))/(sqrt(10) + sqrt(3)) - (2sqrt(5))/(sqrt(6) + sqrt(5)) - (3sqrt(2))/(sqrt(15) + 3sqrt(2)`

Simplify the following :

`(4sqrt(3))/((2 - sqrt(2))) - (30)/((4sqrt(3) - 3sqrt(2))) - (3sqrt(2))/((3 + 2sqrt(3))`

If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.

In the following, find the values of a and b.

`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`

In the following, find the values of a and b:

`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`

In the following, find the values of a and b:

`(5 + 2sqrt(3))/(7 + 4sqrt(3)) = "a" + "b"sqrt(3)`

In the following, find the values of a and b:

`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`

In the following, find the values of a and b:

`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`

In the following, find the values of a and b:

`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`

In the following, find the values of a and b:

`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`

In the following, find the values of a and b:

`(sqrt(2) + sqrt(3))/(3sqrt(2) - 2sqrt(3)) = "a" - "b"sqrt(6)`

In the following, find the value of a and b:

`(7 + sqrt(5))/(7 - sqrt(5)) - (7 - sqrt(5))/(7 + sqrt(5)) = "a" + "b"sqrt(5)`

In the following, find the value of a and b:

`(sqrt(3) - 1)/(sqrt(3) + 1) + (sqrt(3) + 1)/(sqrt(3) - 1) = "a" + "b"sqrt(3)`

If x = `(7 + 4sqrt(3))`, find the value of

`sqrt(x) + (1)/(sqrt(x)`

If x = `(7 + 4sqrt(3))`, find the value of

`x^2 + (1)/x^2`

If x = `(7 + 4sqrt(3))`, find the value of `x^3 + (1)/x^3`.

If x = `(7 + 4sqrt(3))`, find the values of :

`(x + (1)/x)^2`

If x = `(4 - sqrt(15))`, find the values of 

`(1)/x`

If x = `(4 - sqrt(15))`, find the values of

`x + (1)/x`

If x = `(4 - sqrt(15))`, find the values of 

`x^2 + (1)/x^2`

If x = `(4 - sqrt(15))`, find the values of

`x^3 + (1)/x^3`

If x = `(4 - sqrt(15))`, find the values of:

`(x + (1)/x)^2` 

If x = `((2 + sqrt(5)))/((2 - sqrt(5))` and y = `((2 - sqrt(5)))/((2 + sqrt(5))`, show that (x² - y²) = `144sqrt(5)`.

If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of 

x² + y²

If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) + 1)`, find the values of 

x³ + y³

If x = `((sqrt(3) + 1))/((sqrt(3) - 1)` and y = `((sqrt(3) - 1))/((sqrt(3) - 1)`, find the values of 

x² - y² + xy

If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of

x² + y²

If x = `(1)/((3 - 2sqrt(2))` and y = `(1)/((3 + 2sqrt(2))`, find the values of 

x³ + y³