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# Add or subtracting numbers with a power in a root.

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Intern
Joined: 14 Jul 2014
Posts: 7

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09 Aug 2017, 15:15
Hello,

I am having trouble understanding why when factoring in a root you would leave the power to a number in the original number you factored.

Ex. \sqrt{36^2+15^2}. When factoring this the answer noted to keep the power of the factored number. --> \sqrt{3^2(12^2+5^2)}. Can someone please explain to me why it wouldn't look like this --> \sqrt{3^2(12+5)}. Is there a rule I am missing? I noticed that when it involves factoring an expression in a root that it keeps the power, but if it isn't in a root it doesn't. Please correct me if I a wrong here. Please provide a detailed explanation.

Original question: \sqrt{36^2+15^2} simply the root and express answer as an integer.

Best,

Jai
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Joined: 30 Jan 2016
Posts: 1066
Re: Add or subtracting numbers with a power in a root.  [#permalink]

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10 Aug 2017, 02:18
1
jcallahan6 wrote:
Hello,

I am having trouble understanding why when factoring in a root you would leave the power to a number in the original number you factored.

Ex. \sqrt{36^2+15^2}. When factoring this the answer noted to keep the power of the factored number. --> \sqrt{3^2(12^2+5^2)}. Can someone please explain to me why it wouldn't look like this --> \sqrt{3^2(12+5)}. Is there a rule I am missing? I noticed that when it involves factoring an expression in a root that it keeps the power, but if it isn't in a root it doesn't. Please correct me if I a wrong here. Please provide a detailed explanation.

Original question: \sqrt{36^2+15^2} simply the root and express answer as an integer.

Best,

Jai

Hi!

I'm not sure what you exactly mean, but let's go step by step.

$$\sqrt{(36^2+15^2)}$$=$$\sqrt{((3*3*2*2)^2+(3*5)^2)}$$=$$\sqrt{((3^2*2^2)^2+(3*5)^2)}$$=$$\sqrt{3^4*2^4+3^2*5^2}$$=$$\sqrt{3^2(3^2*2^4+5^2)}$$=
$$\sqrt{3^2((3*2^2)^2+5^2)}$$=$$\sqrt{3^2(12^2+5^2)}$$=$$\sqrt{3^2(144+25)}$$=$$\sqrt{3^2(169)}$$=$$\sqrt{3^2*13^2}$$=3*13=69

if you forget how to multiply, use simple numbers: $$3^2*3^2=3*3*3*3=3^4$$. So, basically, you have to add power to power - 2+2.
_________________
Non progredi est regredi
Intern
Joined: 14 Jul 2014
Posts: 7
Re: Add or subtracting numbers with a power in a root.  [#permalink]

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10 Aug 2017, 10:38
Akela wrote:
jcallahan6 wrote:
Hello,

I am having trouble understanding why when factoring in a root you would leave the power to a number in the original number you factored.

Ex. \sqrt{36^2+15^2}. When factoring this the answer noted to keep the power of the factored number. --> \sqrt{3^2(12^2+5^2)}. Can someone please explain to me why it wouldn't look like this --> \sqrt{3^2(12+5)}. Is there a rule I am missing? I noticed that when it involves factoring an expression in a root that it keeps the power, but if it isn't in a root it doesn't. Please correct me if I a wrong here. Please provide a detailed explanation.

Original question: \sqrt{36^2+15^2} simply the root and express answer as an integer.

Best,

Jai

Hi!

I'm not sure what you exactly mean, but let's go step by step.

$$\sqrt{(36^2+15^2)}$$=$$\sqrt{((3*3*2*2)^2+(3*5)^2)}$$=$$\sqrt{((3^2*2^2)^2+(3*5)^2)}$$=$$\sqrt{3^4*2^4+3^2*5^2}$$=$$\sqrt{3^2(3^2*2^4+5^2)}$$=
$$\sqrt{3^2((3*2^2)^2+5^2)}$$=$$\sqrt{3^2(12^2+5^2)}$$=$$\sqrt{3^2(144+25)}$$=$$\sqrt{3^2(169)}$$=$$\sqrt{3^2*13^2}$$=3*13=69

if you forget how to multiply, use simple numbers: $$3^2*3^2=3*3*3*3=3^4$$. So, basically, you have to add power to power - 2+2.

Thank you for the help! I see how you broke it down into primes to better explain this. The book answer left me a bit confused so it was nice to see it this way as as a better way of understanding to use simple numbers.
Re: Add or subtracting numbers with a power in a root.   [#permalink] 10 Aug 2017, 10:38
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