Advertisements
Advertisements
Question
The value of `sqrt(248 + sqrt(52 + sqrt(144)` is ______.
Options
14
12
16
13
Advertisements
Solution
The value of `sqrt(248 + sqrt(52 + sqrt(144)` is 16.
Explanation:
144 = 2 × 2 × 2 × 2 × 3 × 3
= (2 × 2 × 3)2
= 122
∴ `sqrt(144) = 12`
∴ `sqrt(248 + sqrt(52 + sqrt(144))) = sqrt(248 + sqrt(52 + 12))`
= `sqrt(248 +sqrt( 64))` ...(i)
Also, 64 = 2 × 2 × 2 × 2 × 2 × 2
= (2 × 2 × 2)2
= 82
`\implies sqrt(64) = 8`
∴ From (i), we get
`sqrt(248 + sqrt(52 + sqrt(144))) = sqrt(248 + 8`
= `sqrt(256)` ...(ii)
256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= (2 × 2 × 2 × 2)2
= (16)2
`\implies sqrt(256) = 16`
∴ From (ii), we get
`sqrt(248 + sqrt(52 + sqrt(144))) = 16`
APPEARS IN
RELATED QUESTIONS
The students of Class VIII of a school donated Rs 2401 in all, for Prime Minister’s National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.
Find the square root of:
\[23\frac{394}{729}\]
Find the square root of:
\[21\frac{51}{169}\]
The area of a square field is \[80\frac{244}{729}\] square metres. Find the length of each side of the field.
The area of a square field is \[30\frac{1}{4} m^2 .\] Calculate the length of the side of the square.
Find the smallest number by which 10368 be divided, so that the result is a perfect square. Also, find the square root of the resulting numbers.
Find the square root of: 27.3529
For the following, find the least number that must be subtracted so that the resulting number is a perfect square.
796
State, whether the square of the following number is even or odd?
75
Given that `sqrt(4096) = 64`, the value of `sqrt(4096) + sqrt(40.96)` is ______.
