Simplify the root. − 5 1024 -^5\sqrt{1024}

Here we need to simplify the root negative fifth root of 1,024. So to start, let's break down 1,024. Since this is an even number, I know that it's divisible by two. Dividing by two, we get 512. Five twelve is also even, so it's divisible by two, leaving us with 256. 256 is also even, dividing by two we get 128, and 128 divided by two is 64. Now 64 is a perfect square number, we know that that's eight times eight, and that eight breaks down into four times two, as well as two times four. Now I'm going to stop here because already I can tell that I have more than five multiples of the same number. We have a lot of twos, which tells me that two is not the number we're looking for. Instead, let's try and create groupings of four. So I have one four here, a second four here. I can recombine these two twos to make a third four. So we have one, two, three, four so far. I could recombine these two two's to multiply to four, as well as these two two's to multiply to four. And all in all, that now gives me five fours. So that means four to the fifth power is 1,024. So the fifth root of 1,024 is going to equal four And with this negative out front we know that that's going to also be negative four as our final answer.

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Multiple Choice

Simplify the root.
$-^{5} \sqrt{1024}$

$4$

$-4$

$0.16$

$-160$

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검증된 단계별 안내

Identify the expression to simplify: the negative square root of 1024, written as $-\sqrt{1024}$.

Recall that the square root of a number $a$ is a value $b$ such that $b^2 = a$. So, find the number whose square is 1024.

Calculate $\sqrt{1024}$ by recognizing that 1024 is a perfect square (since $32^2 = 1024$).

Apply the negative sign outside the square root to the result found in the previous step, giving $-32$.

Write the simplified expression as $-32$, which is the simplified form of the original expression.

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Struggling with Intermediate Algebra?

Simplify the root.−51024-^5\(\sqrt{1024}\)

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Simplify the root.
$-^{5} \sqrt{1024}$