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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1. Review of Real Numbers2h 43m

Simplifying Fractions
30m

Evaluating Exponents
29m

Evaluating Expressions
15m

Translating Phrases to Expressions
16m

Translating Sentences to Equations
9m

The Distributive Property
17m

Simplifying Expressions
44m

2. Linear Equations and Inequalities5h 35m

Solving Linear Equations
2h 23m

Linear Inequalities in One Variable
46m

Set Operations and Compound Inequalities
1h 7m

Absolute Value Equations
38m

Absolute Value Inequalities
39m

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37m

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25m

Percent Problem Solving
59m

Mixture Problem Solving
43m

4. Graphs and Functions5h 12m

The Rectangular Coordinate System
44m

Graph Linear Equations in Two Variables
24m

Graph Linear Equations Using Intercepts
23m

Slope of a Line
44m

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38m

Point Slope Form
22m

Linear Inequalities in Two Variables
28m

Introduction to Relations and Functions
53m

Function Notation
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Composition of Functions
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45m

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23m

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The Product Rule
9m

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10m

Intro to the Power Rules
17m

The Power of a Quotient Rule
13m

Negative Exponents
24m

Simplifying Exponential Expressions Using All Exponent Rules
6m

Intro to Polynomials
21m

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38m

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34m

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37m

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Factoring Trinomials of the Form ax² + bx + c
37m

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41m

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41m

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42m

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25m

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19m

Least Common Denominators
32m

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32m

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44m

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Introduction to Radical Expressions
47m

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47m

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19m

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53m

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18m

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51m

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25m

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40m

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29m

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9. Roots, Radicals, and Complex Numbers

Introduction to Radical Expressions

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9. Roots, Radicals, and Complex Numbers

Introduction to Radical Expressions

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Multiple Choice

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

$4$

$-4$

$0.16$

$-160$

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Verified step by step guidance

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.
$-^{5} \sqrt{1024}$