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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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Vikki [24]

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3 0
2 years ago
Now given a rope hanging from the top of a pole. The end lying on the ground is 3 chi long. When tightly stretchedit is 8 chi fr
drek231 [11]

Answer:

Height of the pole = 9.17 chi.

Length of the rope = 12.17 chi.

Step-by-step explanation:

Given that the rope is hanging from the top of a pole having height x chi and the portion of the rope lying on the ground is 3 chi.

So, the length of the rope= x + 3 chi.

Let AB represents the pole in the figure, and one end of the rope is at point A.

When the rope is tightly stretched, let C be the other end of the rope as shown in the triangle.

The length of the rope = AC.

\Rightarrow AC=x+3 chi.

Distance from the bottom of the pole, point A, to the other end of the pole, point B, is 8 chi.

So, BC=8 chi.

As the triangle ABC is a right-angled triangle, so by using Pythagoras theorem,

AC^2= AB^2+BC^2

\Rightarrow (x+3)^2=x^2+8^2

\Rightarrow x^2+6x+9=x^2+64

\Rightarrow 6x=64-9=55

\Rightarrow x=55/6=9.17 chi.

Hence, the height of the pole, AB=x=9.17 chi,

and the length of the rope, x+3=9.17+3=12.17 chi.

8 0
3 years ago
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