Question

a) Evaluate $\sqrt{a^{2}}$ for $a=1.3$. b) Evaluate $\sqrt{a^{2}}$ for $a=-1.3$.

Name: Problem 111, Chapter 7: Intermediate Algebra for College Students
Uploaded: 2021-07-09T20:51:46-08:00
Duration: 1 min 4 s
Channel: Julie Silva
Description: a) Evaluate √(a^2) for a=1.3. b) Evaluate √(a^2) for a=-1.3.

   a) Evaluate $\sqrt{a^{2}}$ for $a=1.3$.
b) Evaluate $\sqrt{a^{2}}$ for $a=-1.3$.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 7, Problem 111

Instant Answer

Solved by Expert Julie Silva

07/09/2021

Step 1

3$, we first find $a^2$: $1.3^2 = 1.3 \times 1.3 = 1.69$ Now, we find the square root of $1.69$: $\sqrt{1.69} = 1.3$ So, $\sqrt{a^{2}} = 1.3$ when $a=1.3$. Show more…

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a) Evaluate $\sqrt{a^{2}}$ for $a=1.3$. b) Evaluate $\sqrt{a^{2}}$ for $a=-1.3$.

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Key Concepts

Square Root Function

The square root function, commonly denoted as ?x, returns the principal (nonnegative) square root of a nonnegative number x. It is defined only for nonnegative real numbers, ensuring that the output is also nonnegative.

Absolute Value

The absolute value function, denoted as |a|, measures the distance of a number a from zero on the number line without considering its sign. It directly relates to the identity ?(a²) = |a|, which means that regardless of whether a is positive or negative, taking the square of the number and then its square root will yield the nonnegative magnitude of a.

Square Function

The square function takes a number and multiplies it by itself. This operation always results in a nonnegative number, regardless of whether the original number was positive or negative, due to the properties of real number multiplication.

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