Square Root
When y = x2 then square root of y is x and it is written as √y = x.
For example, √9 = 3, √16 = 4 and so on.
Cube Root
When y = x3 then cube root of y is x and it is written as ∛y = x.
For example, ∛8 = 2, ∛27 = 3 and so on.
Important Formulaes
√ab = √a x √b
√(a/b) = √a / √b
Solved Examples
Answer - A
Explanation
Resolve 2025 into prime numbers first. 2025 = 5 x 5 x 3 x 3 x 3 x 3 = 52 x 32 x 32 ∴ √2025 = 5 x 3 x 3 = 45
Answer - C
Explanation
√ 54 x √ 6 = √ 54 x 6 = √ (3 x 3 x 6 x 6) = √ (32 x 62) = √ 18
Answer - D
Explanation
√(248 + √(51 + √169)) = √(248 + √(51 + 13)) = √(248 + √(64)) = √(248 + 8) = √(256) = 16
Answer - B
Explanation
√(25/16) = √25/ √ 16 = 5/4.
Answer - B
Explanation
√(5/3) = (√5 / √ 3) x (√3 / √ 3) = √15 / 3 = 3.88/ 3 = 1.293
Q 6 - If √ 1369 = 37 then what is √13.69 + √0.1369 + √ 0.001369 + √ 0.00001369?
Answer - B
Explanation
√13.69 + √0.1369 + √ 0.001369 + √ 0.00001369 = √(1369 / 100) + √(1369/ 10000) + √(1369/ 1000000) + √(1369/ 100000000) = √1369 / √100 + √1369 / √10000 + √1369 / √1000000 + √1369 / √100000000 = 37/10 + 37/100 + 37/1000 + 37/ 10000 = 3.7 + 0.37 + 0.037 + 0.0037 = 4.1107
Answer - A
Explanation
(√5 + √3)/(√5 - √3) = (√5 + √3)/(√5 - √3) * (√5 + √3)/(√5 + √3) = (√5 + √3)2/(5 - 3) = (5 + 3 + 2√5 + √3)/2 = (8 + 2√15)/2 = 2(4 + √15)/2 = 4 + √15 = 4 + 3.8729 = 7.8729
Answer - A
Explanation
9261 = 3 x 3 x 3 x 7 x 7 x 7 = 33 x 73 ∴ ∛9261 = (33 x 73)1/3 = 3 x 7 = 21.
Q 9 - What is the least number required to multiply to 9720 to make a perfact cube?
Answer - C
Explanation
9261 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 3 x 3 = 23 x 33 x 32 x 5 ∴ required no: 3 x 52 = 3 x 25 = 75
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