# Solution - Operations on Real Numbers

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ConceptOperations on Real Numbers

#### Question

Rationalise the denominators of the following :-

(i) 1/sqrt7

(ii) 1/(sqrt7-sqrt6)

(iii) 1/(sqrt5+sqrt2)

(iv) 1/(sqrt7-2)

#### Solution

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#### Similar questions

Classify the following numbers as rational or irrational :-

(i) 2-sqrt5

(ii) (3+sqrt23)-sqrt23

(iii) (2sqrt7)/(7sqrt7)

(iv) 1/sqrt2

(v) 2π

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Recall, π is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is, π = c/d. This seems to contradict the fact that p is irrational. How will you resolve this contradiction?

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Represent sqrt9.3  on the number line.

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Simplify each of the following expressions :-

(i) (3+sqrt3)(2+sqrt2)

(ii) (3+sqrt3)(3-sqrt3)

(iii) (sqrt5+sqrt2)^2

(iv) (sqrt5-sqrt2)(sqrt5+sqrt2)

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