Math / Numbers & Operations

Question\begin{align} \text{a) } & \frac{75}{5 \sqrt{3}} ; \frac{42}{7 \sqrt{2}} ; \frac{18}{3 \sqrt{2}} ; \frac{45}{5 \sqrt{3}} ; \frac{36}{4 \sqrt{3}} ; \frac{24}{2 \sqrt{6}} ; \frac{6}{3 \sqrt{2}} ; \frac{15}{\sqrt{3}}; \\ \text{b) } & \frac{28}{4 \sqrt{7}} ; \frac{24}{4 \sqrt{6}} ; \frac{18}{6 \sqrt{3}} ; \frac{36}{6 \sqrt{6}} ; \frac{54}{9 \sqrt{6}} ; \frac{72}{9 \sqrt{8}} ; \frac{30}{15 \sqrt{2}} ; \frac{42}{6 \sqrt{7}}; \\ \text{c) } & \frac{8}{3 \sqrt{2}} ; \frac{6}{\sqrt{3}} ; \frac{24}{5 \sqrt{6}} ; \frac{15}{2 \sqrt{3}} ; \frac{4}{3 \sqrt{2}} ; \frac{28}{3 \sqrt{7}} ; \frac{12}{5 \sqrt{2}} ; \frac{10}{3 \sqrt{5}}; \\ \text{d) } & \frac{12}{5 \sqrt{6}} ; \frac{15}{5 \sqrt{3}} ; \frac{18}{\sqrt{24}} ; \frac{25}{4 \sqrt{5}} ; \frac{15}{2 \sqrt{5}} ; \frac{30}{7 \sqrt{6}} ; \frac{45}{2 \sqrt{10}} ; \frac{8}{3 \sqrt{6}} ; \frac{9}{2 \sqrt{6}}; \\ \text{e) } & \frac{18}{2 \sqrt{6}} ; \frac{45}{5 \sqrt{3}} ; \frac{3}{\sqrt{12}} ; \frac{9}{\sqrt{27}} ; \frac{12}{\sqrt{48}} ; \frac{24}{10 \sqrt{6}} ; \frac{15}{3 \sqrt{6}} ; \frac{18}{3 \sqrt{54}}. \end{align}

Studdy Solution

STEP 1

1. We are given a list of fractions with square roots in the denominators.
2. The task is to simplify each fraction by rationalizing the denominator.

STEP 2

1. Identify the fractions to be simplified.
2. Rationalize the denominator for each fraction.
3. Simplify the resulting expression.

STEP 3

Identify the fractions in each group that need to be simplified. Each fraction is of the form $\frac{a}{b \sqrt{c}}$ .

STEP 4

For each fraction $\frac{a}{b \sqrt{c}}$ , multiply both the numerator and the denominator by $\sqrt{c}$ to rationalize the denominator.
Example: For $\frac{75}{5 \sqrt{3}}$ , multiply by $\frac{\sqrt{3}}{\sqrt{3}}$ .
$\frac{75}{5 \sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{75 \sqrt{3}}{5 \times 3}$

STEP 5

Calculate the new denominator and simplify the fraction.
Example: Continuing from the previous step:
$\frac{75 \sqrt{3}}{15} = \frac{75}{15} \times \sqrt{3} = 5 \sqrt{3}$

STEP 6

Repeat the rationalization and simplification process for each fraction in the list.
Example: For $\frac{42}{7 \sqrt{2}}$ :
$\frac{42}{7 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{42 \sqrt{2}}{7 \times 2} = \frac{42 \sqrt{2}}{14} = 3 \sqrt{2}$

STEP 7

Continue simplifying each fraction in the list using the same method.
Example: For $\frac{18}{3 \sqrt{2}}$ :
$\frac{18}{3 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{18 \sqrt{2}}{3 \times 2} = \frac{18 \sqrt{2}}{6} = 3 \sqrt{2}$
Repeat the above steps for all fractions in groups b), c), d), and e) until all fractions are simplified.

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Studdy Solution

STEP 1

1. We are given a list of fractions with square roots in the denominators.
2. The task is to simplify each fraction by rationalizing the denominator.

STEP 2

1. Identify the fractions to be simplified.
2. Rationalize the denominator for each fraction.
3. Simplify the resulting expression.

STEP 3

Identify the fractions in each group that need to be simplified. Each fraction is of the form $\frac{a}{b \sqrt{c}}$ .

STEP 4

STEP 5

Calculate the new denominator and simplify the fraction.
Example: Continuing from the previous step:
$\frac{75 \sqrt{3}}{15} = \frac{75}{15} \times \sqrt{3} = 5 \sqrt{3}$

STEP 6

Repeat the rationalization and simplification process for each fraction in the list.
Example: For $\frac{42}{7 \sqrt{2}}$ :
$\frac{42}{7 \sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{42 \sqrt{2}}{7 \times 2} = \frac{42 \sqrt{2}}{14} = 3 \sqrt{2}$

STEP 7

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Studdy Solution

STEP 1

1. We are given a list of fractions with square roots in the denominators.2. The task is to simplify each fraction by rationalizing the denominator.

STEP 2

1. Identify the fractions to be simplified.2. Rationalize the denominator for each fraction.3. Simplify the resulting expression.

STEP 3

Identify the fractions in each group that need to be simplified. Each fraction is of the form abc\frac{a}{b \sqrt{c}}bc​a​.

STEP 4

STEP 5

Calculate the new denominator and simplify the fraction.Example: Continuing from the previous step:75315=7515×3=53\frac{75 \sqrt{3}}{15} = \frac{75}{15} \times \sqrt{3} = 5 \sqrt{3}15753​​=1575​×3​=53​

STEP 6

STEP 7

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We are given a list of fractions with square roots in the denominators.
2. The task is to simplify each fraction by rationalizing the denominator.

1. Identify the fractions to be simplified.
2. Rationalize the denominator for each fraction.
3. Simplify the resulting expression.

Identify the fractions in each group that need to be simplified. Each fraction is of the form $\frac{a}{b \sqrt{c}}$ .

Calculate the new denominator and simplify the fraction.
Example: Continuing from the previous step:
$\frac{75 \sqrt{3}}{15} = \frac{75}{15} \times \sqrt{3} = 5 \sqrt{3}$