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Consider this expression.
[tex]\[ \sqrt{a^3-7} + |b| \][/tex]

When [tex]\( a=2 \)[/tex] and [tex]\( b=-4 \)[/tex], the value of the expression is [tex]\( \boxed{} \)[/tex]



Answer :

GinnyAnswer
To find the value of the expression [tex]\(\sqrt{a^3 - 7} + |b|\)[/tex] when [tex]\(a = 2\)[/tex] and [tex]\(b = -4\)[/tex], follow these steps:

1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[ a^3 = 2^3 = 8 \][/tex]

2. Substitute [tex]\(a^3\)[/tex] into the expression [tex]\(a^3 - 7\)[/tex]:
[tex]\[ a^3 - 7 = 8 - 7 = 1 \][/tex]

3. Find the square root of [tex]\(1\)[/tex]:
[tex]\[ \sqrt{1} = 1.0 \][/tex]

4. Calculate the absolute value of [tex]\(b\)[/tex]:
[tex]\[ |b| = |-4| = 4 \][/tex]

5. Add the results from step 3 and step 4:
[tex]\[ 1.0 + 4 = 5.0 \][/tex]

Therefore, the value of the expression when [tex]\(a=2\)[/tex] and [tex]\(b=-4\)[/tex] is [tex]\(5.0\)[/tex].

Answer: 5

Step-by-step explanation:

First, plug in the numerical values of the variables and rewrite the equation:

[tex]\sqrt{a^{3} - 7 } +|b|[/tex] = [tex]\sqrt{2^{3} - 7 } +|-4|[/tex]

Next, solve for the equation under the radical [tex](\sqrt{ } )[/tex] symbol:

[tex]\sqrt{2^{3} - 7 } = \sqrt{8 - 7 } = \sqrt{1}[/tex] = 1

The equation is now [tex]1+ |-4|[/tex]

Absolute value is distance between a number and zero. It is represented by | n |, where n is a positive or negative integer. To learn more about absolute value, visit https://brainly.com/question/12928519

Now, with this is mind, you can find the absolute value of -4. -4 is 4 units away from zero, meaning [tex]|-4| = 4[/tex].

The final equation is 1 + 4. The value of the expression is 5