OPERATIONS WITH EXPONENTS AND RADICALS

Problem 1 :

Which is equivalent to 49^3/2 ?

Solution :

So, option D. is correct.

Problem 2 :

Which expression is another way to write ∛125x⁴ ?

Solution :

So, option B. is correct.

Problem 3 :

If x and y are real numbers, what is the simplified radical form of (x²y⁵)^1/5 ?

Solution :

So, option A. is correct. 

Problem 4 :

What is the simplified expression of √(36x⁸/4x⁶) ?

Solution :

So, option A. is correct. 

Problem 5 :

What is the simplified form of (2√5 + 3) (√5 - 1) ?

Solution :

Given, (2√5 + 3) (√5 - 1)

= √5(2√5) - 2√5 + 3√5 - 3

= 2(5) + √5 - 3

= 10 + √5 - 3

= √5 + 7

So, option B. is correct. 

Problem 6 :

Solution :

So, option B. is correct. 

Problem 7 :

The area of a square is 2√2 + 3. What is the length of a side of the square ?

Solution :

area of a square = s²

2√2 + 3 = s²

Taking square root on both sides.

So, option B. is correct. 

Problem 7 :

Which expression is equivalent to √-6(√-4 - √3) ? 

Solution :

Given, √-6(√-4 - √3)

= √-6 × √-4 - (√-6 × √3)

=  √24 - √-18

= (√6 × √4) - (√-9 × √2)   

= 2√6 - 3i√2

So, option C. is correct.