Question

Please help me on this

Answer 1

The answer is D because the square root of 3^15 is 2187 square root of 3. Now if you add 3^7 then that gives you 2187. So your answer would be D

Answer 2

Hello!

The answer is:

The correct option is D. $\sqrt{3^{15} }=3^{7}* \sqrt{3}$

Why?

To solve this problem, we must remember the following properties:

Product of powers with the same base:

$a^{m}a^{n}=a^{m+n}$

Power of a power:

$(a^{m})^{n}=a^{m*n}$

Also, we must remember that if we want to introduce a number into a root, in order to not change the expression, we need to introduce it with the same exponent:

$a*\sqrt{b}=\sqrt{a^{2}*b }$

So, solving the problem, we have:

$\sqrt{3^{15} }=3^{7}*\sqrt{3}\\\\3^{7}*\sqrt{3}=\sqrt{(3^{7})^{2} *3}\\\\\sqrt{(3^{7})^{2} *3}=\sqrt{(3^{14} *3}\\\\\sqrt{3^{14} *3}=\sqrt{3^{14+1}$

$\sqrt{3^{14+1} } =\sqrt{3^{15}}$

Hence,

$\sqrt{3^{15} }=3^{7}* \sqrt{3}$

So, the correct option is D. $\sqrt{3^{15} }=3^{7}* \sqrt{3}$

Have a nice day!