College

Complete the expressions and determine the shape: ległobok, trapez, or romb.

c) [tex]\sqrt{1 \frac{11}{25}} - \sqrt[3]{-0.001} = \qquad[/tex]
d) [tex]-2 \sqrt{5} - 5 \sqrt{5} = \qquad[/tex]

Answer :

Sure, let's solve the problems step-by-step:

### For part c:

You need to evaluate the expression:

[tex]\[ \sqrt{1 \frac{11}{25}} - \sqrt[3]{-0.001} \][/tex]

1. First, simplify the mixed number in the square root:
[tex]\[
1 \frac{11}{25} = 1 + \frac{11}{25}
\][/tex]

2. Convert the mixed number to an improper fraction:
[tex]\[
1 + \frac{11}{25} = \frac{25}{25} + \frac{11}{25} = \frac{36}{25}
\][/tex]

3. Calculate the square root of [tex]\(\frac{36}{25}\)[/tex]:
[tex]\[
\sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5} = 1.2
\][/tex]

4. Calculate the cube root of -0.001:
[tex]\[
\sqrt[3]{-0.001} = -0.1
\][/tex]

5. Now perform the subtraction:
[tex]\[
1.2 - (-0.1) = 1.2 + 0.1 = 1.3
\][/tex]

So, the answer for part c is:
[tex]\[ 1.3 \][/tex]

### For part d:

You need to evaluate the expression:

[tex]\[ -2 \sqrt{5} - 5 \sqrt{5} \][/tex]

1. Calculate each term separately:

- First term:
[tex]\[
-2 \sqrt{5}
\][/tex]

- Second term:
[tex]\[
-5 \sqrt{5}
\][/tex]

2. Combine the terms:
Since both terms have the common factor [tex]\(\sqrt{5}\)[/tex], you can add the coefficients:
[tex]\[
-2 \sqrt{5} - 5 \sqrt{5} = (-2 - 5) \sqrt{5} = -7 \sqrt{5}
\][/tex]

So, the answer for part d is:
[tex]\[ -7 \sqrt{5} \][/tex]

I hope this helps! If you have any more questions or need further clarification, feel free to ask!

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