# 5.7 Simplify and use square roots  (Page 8/8)

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$180$ calories per $8$ ounces

$90$ pounds per $7.5$ square inches

$\frac{90\phantom{\rule{0.2em}{0ex}}\text{pounds}}{7.5\phantom{\rule{0.2em}{0ex}}\text{square inches}}$

$126$ miles in $4$ hours

$\text{612.50}$ for $35$ hours

$\frac{\text{612.50}}{35\phantom{\rule{0.2em}{0ex}}\text{hours}}$

Find Unit Rates

In the following exercises, find the unit rate.

$180$ calories per $8$ ounces

$90$ pounds per $7.5$ square inches

12 pounds/sq.in.

$126$ miles in $4$ hours

$\text{612.50}$ for $35$ hours

$17.50/hour Find Unit Price In the following exercises, find the unit price. t-shirts: $3$ for $\text{8.97}$ Highlighters: $6$ for $\text{2.52}$$0.42

An office supply store sells a box of pens for $\text{11}.$ The box contains $12$ pens. How much does each pen cost?

Anna bought a pack of $8$ kitchen towels for $\text{13.20}.$ How much did each towel cost? Round to the nearest cent if necessary.

$1.65 In the following exercises, find each unit price and then determine the better buy. Shampoo: $12$ ounces for $\text{4.29}$ or $22$ ounces for $\text{7.29}?$ Vitamins: $60$ tablets for $\text{6.49}$ or $100$ for $\text{11.99}?$$0.11, $0.12; 60 tablets for$6.49

Translate Phrases to Expressions with Fractions

In the following exercises, translate the English phrase into an algebraic expression.

$535$ miles per $h\phantom{\rule{0.2em}{0ex}}\text{hours}$

$a$ adults to $45$ children

$\frac{a\phantom{\rule{0.2em}{0ex}}\text{adults}}{45\phantom{\rule{0.2em}{0ex}}\text{children}}$

the ratio of $4y$ and the difference of $x$ and $10$

the ratio of $19$ and the sum of $3$ and $n$

$\frac{19}{3+n}$

## Simplify and Use Square Roots

Simplify Expressions with Square Roots

In the following exercises, simplify.

$\sqrt{64}$

$\sqrt{144}$

12

$-\sqrt{25}$

$-\sqrt{81}$

−9

$\sqrt{-9}$

$\sqrt{-36}$

not a real number

$\sqrt{64}+\sqrt{225}$

$\sqrt{64+225}$

17

Estimate Square Roots

In the following exercises, estimate each square root between two consecutive whole numbers.

$\sqrt{28}$

$\sqrt{155}$

$12<\sqrt{155}<13$

Approximate Square Roots

In the following exercises, approximate each square root and round to two decimal places.

$\sqrt{15}$

$\sqrt{57}$

7.55

Simplify Variable Expressions with Square Roots

In the following exercises, simplify. (Assume all variables are greater than or equal to zero.)

$\sqrt{{q}^{2}}$

$\sqrt{64{b}^{2}}$

8 b

$-\sqrt{121{a}^{2}}$

$\sqrt{225{m}^{2}{n}^{2}}$

15 mn

$-\sqrt{100{q}^{2}}$

$\sqrt{49{y}^{2}}$

7 y

$\sqrt{4{a}^{2}{b}^{2}}$

$\sqrt{121{c}^{2}{d}^{2}}$

11 cd

Use Square Roots in Applications

In the following exercises, solve. Round to one decimal place.

Art Diego has $225$ square inch tiles. He wants to use them to make a square mosaic. How long can each side of the mosaic be?

Landscaping Janet wants to plant a square flower garden in her yard. She has enough topsoil to cover an area of $30$ square feet. How long can a side of the flower garden be?

5.5 feet

Gravity A hiker dropped a granola bar from a lookout spot $576$ feet above a valley. How long did it take the granola bar to reach the valley floor?

Accident investigation The skid marks of a car involved in an accident were $216$ feet. How fast had the car been going before applying the brakes?

72 mph

## Chapter practice test

Write six and thirty-four thousandths as a decimal.

Write $1.73$ as a fraction.

$1\frac{73}{100}$

Write $\frac{5}{8}$ as a decimal.

Round $16.749$ to the nearest tenth hundredth whole number

1. 16.7
2. 16.75
3. 17

Write the numbers $\frac{4}{5},-0.1,0.804,\frac{2}{9},-7.4,0.21$ in order from smallest to largest.

In the following exercises, simplify each expression.

$15.4+3.02$

18.42

$20-5.71$

$\left(0.64\right)\left(0.3\right)$

0.192

$\left(-4.2\right)\left(100\right)$

$0.96÷\left(-12\right)$

−0.08

$-5÷0.025$

$-0.6÷\left(-0.3\right)$

2

${\left(0.7\right)}^{2}$

$24÷\left(0.1+0.02\right)$

200

$4\left(10.3-5.8\right)$

$1.6+\frac{3}{8}$

1.975

$\frac{2}{3}\left(14.65-4.6\right)$

In the following exercises, solve.

$m+3.7=2.5$

−1.2

$\frac{h}{0.5}=4.38$

$-6.5y=-57.2$

8.8

$1.94=a-2.6$

Three friends went out to dinner and agreed to split the bill evenly. The bill was $\text{79.35}.$ How much should each person pay?

$26.45 A circle has radius $12.$ Find the circumference and area. $\text{[}\text{Use}\phantom{\rule{0.2em}{0ex}}3.14\phantom{\rule{0.2em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}\pi \text{.]}$ The ages, in months, of $10$ children in a preschool class are: $55$ , $55$ , $50$ , $51$ , $52$ , $50$ , $53$ , $51$ , $55$ , $49$ Find the mean median mode 1. 59 2. 51.5 3. 55 Of the $16$ nurses in Doreen’s department, $12$ are women and $4$ are men. One of the nurses will be assigned at random to work an extra shift next week. Find the probability a woman nurse will be assigned the extra shift. Convert the fraction to a decimal. Find each unit price and then the better buy. Laundry detergent: $64$ ounces for $\text{10.99}$ or $48$ ounces for $\text{8.49}$ 64 ounces for$10.99 is the better buy

In the following exercises, simplify.

$\sqrt{36+64}$

$\sqrt{144{n}^{2}}$

12 n

Estimate $\sqrt{54}$ to between two whole numbers.

Yanet wants a square patio in her backyard. She has $225$ square feet of tile. How long can a side of the patio be?

15 feet

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