Question

What is the simplified form of 3 StartRoot 135 EndRoot?

Answer 1

Answer:

$9 \sqrt{135}$

Step-by-step explanation:

Express 135 as a product of 15 and 9:

$135=15*9$

So:

$3\sqrt{15*9}$

Now, use the following property:

$\sqrt[n]{a*b} =\sqrt[n]{a}\hspace{3} \sqrt[n]{b}$

Therefore:

$3\sqrt{15} \sqrt{9}$

Since the square root of 9 is 3, the simplified form of $3\sqrt{135}$:

$3\sqrt{15} \sqrt{9}=3*3\sqrt{15} =9\sqrt{15}$

Answer 2

$\bf 3\sqrt{135}~~ \begin{cases} 135=&3\cdot 3\cdot 15\\ &3^2\cdot 15 \end{cases}\implies 3\sqrt{3^2\cdot 15}\implies 9\sqrt{15}$