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yawa3891 [41]
3 years ago
13

Please help me on this

Mathematics
2 answers:
earnstyle [38]3 years ago
6 0
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
Liula [17]3 years ago
4 0
<h2>Hello!</h2>

The answer is:

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

<h2>Why?</h2>

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!

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