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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

Verified Answer :

Ckaranja

5 times b times the square root of 6 times b;
\(\sqrt{150* b^{3} }\)
\(\sqrt{25*6* b^{3} }\)
=5b\(\sqrt{6b}\)

Answer:

The simplified form of the given expression is:

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

Step-by-step explanation:

We are given a expression in  words as:

     square root 150 times b cubed.

Now mathematically it is expressed as:

   \(\sqrt{150b^3}\)

Now on simplifying as follows:

\(\sqrt{150b^3}=\sqrt{5^2\times 3\times 2\times b^2\times b}\\\\\sqrt{150b^3}=\sqrt{(5b)^2\times 6b}\\\\\sqrt{150b^3}=\sqrt{(5b)^2}\times \sqrt{6b}\\\\\sqrt{150b^3}=5b\sqrt{6b}\)

Hence, we obtain the expression:

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

(i.e.  \(5b\sqrt{6b}\)   )

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