Square and cube roots problems with solution

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Introduction

Nithra Jobs assists individuals in preparing for their competitive exams by offering square roots and cube roots questions. Knowledge of square roots and cube roots is important for candidates who are preparing for banking exams or other related courses, If you're struggling with solving problems related to square and cube roots Nithra Jobs will be helpful by providing you with examples of the square roots and cube roots problems with solutions. Take a look at the example sums we've provided and use them as a reference to ace your exams.

Formulas:

Square root

If x² = y, we say that the square root of y is x and we write √y = x.

Ex:

1. √4 = 2, √9 = 3

Cube root

The cube root of a given number x is the number whose cube is x. We denote the cube root of x by ∛x.

Solved Problems

1. The square root of (6 + 4 √2) (6 - 4 √2 ) is?

Answer: 2

Explanation:

Given,

To find the value of √( 6 + 4 √2 ) ( 6 - 4 √2 )

Formula, ( a + b ) ( a - b ) = a² - b²

Using the formula,

√( 6 + 4 √2 ) ( 6 - 4 √2 ) = √[ 6² - ( 4 √2 )² ]

= √36 - (16 × 2)

= √( 36 - 32 )

= √4

= 2

The square root of ( 6 + 4 √2 ) ( 6 - 4 √2 ) is 2.

2. If √3 = 1.732, then the value of ( √3 / 2 ) - ( 6 / √3 ) + √27 is equal to?

Answer: ( 3 √3 ) / 2

Explanation:

( √3 / 2 ) - ( 6 / √3 ) + √27 = ( √3 / 2 ) - ( 6 / √3 ) + √( 3 * 3 * 3 )

= ( √3 / 2 ) - ( 6 / √3 ) + 3 √3

By taking LCM we get,

= [ ( √3 * √3 ) - 12 + ( 3 √3 * 2 √3 ) ] / 2 √3

= [ 3 - 12 + 18 ] / 2 √3

= 9 / 2 √3

= ( 3 * 3 ) / 2 √3

= (√3 * √3 * 3 ) / 2 √3

= ( 3 √3 ) / 2

The value of ( √3 / 2 ) - ( 6 / √3 ) + √27 is ( 3 √3 ) / 2.

3. [ √( 0.0196 * ? ) ] = 1.4

Answer: 100

Explanation:

Let [ √( 0.0196 * x ) ] = 1.4

Then, ( 0.0196 * x ) = ( 1.4 )²

( 0.0196 * x ) = 1.96

x = 1.96 / 0.0196

To remove decimal multiply both sides by 10,000

= 19600 / 196

= 100

The value of x is 100.

4. [ √( 278 + √121 ) ] = ?

Answer: 17

Explanation:

[ √( 278 + √121 ) ] = [ √( 278 + 11 ) ]

= √289

= 17

The value of [ √( 278 + √121 ) ] is 17.

5. One-third of the cube-root of which number is 0.5?

Answer: 3.375

Explanation:

Let the number be n So, ( 1 / 3 ) * ∛n = 0.5

∛n = 0.5 * 3

∛n = 1.5

n = ( 1.5 )³

= (1.5) * (1.5) * (1.5)

= 3.375

The value of ∛n is 3.375.

Conclusion

Here you have seen the above-given square and square root sums and cube and cube root sums with the answers. We hope these Square root and cube root questions with answers will be helpful for your future studies. Stay connected with us to learn more about square and cube formulas and exercises. Nithra Jobs wishes you all the best in your career endeavors. These Square roots and cube roots problems are very helpful and useful for your competitive exam, try it.