Question

Question 1

Which expression is the simplified form of the square root 150 times b cubed?

6 times b times the square root of 5 times b

5 times b times the square root of 6

6 times b times the square root of 5

5 times b times the square root of 6 times b

Answer 1

The simplified form of the given expression is:

5 times b times the square root of 6 times b .

Explanation:

We are given a expression in words as:

square root 150 times b cubed.

Now mathematically it is expressed as:

`√(150b^3)`

Now on simplifying as follows:

`√(150b^3)=√(5^2* 3* 2* b^2* b)\\\\√(150b^3)=√((5b)^2* 6b)\\\\√(150b^3)=√((5b)^2)* √(6b)\\\\√(150b^3)=5b√(6b)`

Hence, we obtain the expression:

5 times b times the square root of 6 times b .

(i.e.
`5b√(6b)` )

Answer 2

5 times b times the square root of 6 times b;

`\sqrt{150* b^(3) }`

`\sqrt{25*6* b^(3) }`
=5b
`√(6b)`