Simplify the following expression: \$(10a\sqrt(36b^3)) / (12\sqrt(25ab))\$.

The given expression is

\$(10a\sqrt(36b^3)) / (12\sqrt(25ab))\$

Simplify the square roots in the numerator and denominator:

\$\sqrt(36b^3) = \sqrt(36) . \sqrt(b^3) = 6b^(3/2)\$

\$\sqrt(25ab) = \sqrt(25) . \sqrt(ab) = 5\sqrt(ab)\$

Substitute these simplified values back into the expression:

\$(10a . 6b^(3/2)) / (12 . 5 \sqrt(ab))\$

\$(60ab^(3/2)) / (60(ab)^(1/2))\$

\$(ab^(3/2)) / (a^(1/2) . b^(1/2))\$

Make it simplify

\$a^(1 - 1/2) . b^(3/2 - 1/2)\$

\$a^(1/2) . b^(2/2)\$

\$b \sqrt(a)\$

So, therefore the simplified expression is \$b\sqrt(a)\$.

Option A is correct because after simplifying the original expression, we obtained \$b\sqrt(a)\$

\$b\sqrt(a)\$

The expression \$\sqrt(ab)\$ is incorrect as it doesn’t correspond to the simplified outcome

\$\sqrt(ab)\$

It incorrectly places a under the square root with b, whereas our simplified form has a and b under the same square root symbol

\$a\sqrt(b)\$

The radical terms and their simplification lead to an answer involving both b and \$\sqrt(a)\$, not just ab. So, it is wrong

ab

Option

A

Can you summarize what you’ve understood in the above steps?