Go through the Math in Focus Grade 8 Workbook Answer Key Chapter 1 Lesson 1.6 Real-World Problems: Squares and Cubes to finish your assignments.

## Math in Focus Grade 7 Course 3 A Chapter 1 Lesson 1.6 Answer Key Real-World Problems: Squares and Cubes

### Math in Focus Grade 8 Chapter 1 Lesson 1.6 Guided Practice Answer Key

**Solve. Show your work.**

Question 1.

Find the two square roots of 169.

Answer:

Explanation:

Given to find two square roots of 169 and -169,So using prime factorization

we get for 169 it is 13 and for – 169 it is -13

**Solve. Show your work.**

Question 2.

Find the cube root of \(\frac{1}{729}\).

Answer:

1/9,

Explanation:

**Solve. Show your work.**

Question 3.

x^{2} = 2.25

x^{2} = 2.25

Answer:

1.5,

Explanation:

**Solve. Show your work.**

Question 4.

Answer:

x = (1/2),

Explanation:

Question 5.

A square field has an area of 98.01 square meters. Find the length of each side of the field.

Let the length of each side be x meters.

x^{2} = Translate into an equation.

= Solve for x by taking the positive root of both sides.

x = m Use a calculator to find the square root.

The length of each side is meters.

Answer:

x^{2} = 98.01 We translate into an equation:

\(\sqrt{x^{2}}\) = \(\sqrt{98.01}\) We solve for x by taking the positive square root of both sides:

x = 9.9m We use a calculator to find the square root:

The length of each side is 9.9 meters.

9.9 meters

**Solve. Show your work.**

Question 6.

Robin bought a crystal globe that has a volume of 1,774\(\frac{2}{3} \pi\)ir cubic centimeters. Find the radius of the crystal globe.

Let the radius of the crystal globe be r centimeters.

Answer:

The radius of the crystal globe is 29.7 cms,

Explanation:

Question 7.

A spherical waterme’on has a volume of 562.5π cubic centimeters. What is the diameter of the watermelon?

Let the radius of the watermelon be r centimeters.

Answer:

The diameter of the watermelon is 15 centimeters,

Explanation:

### Math in Focus Course 3A Practice 1.6 Answer Key

**Find the two square roots of each number. Round your answer to the nearest tenth when you can.**

Question 1.

25

Answer:

5, or -5,

Explanation:

Given to find sqaure roots of 25

1. 5 X 5 = 25,

2. -5 X -5 = 25,

so 5, or -5.

Question 2.

64

Answer:

8 or -8,

Explanation:

Given to find sqaure roots of 64

1. 8 X 8 = 64,

2. -8 X -8 = 64,

so 8, or -8.

Question 3.

80

Answer:

8.944 or -8.944,

Explanation:

Given to find sqaure roots of 64

1. 8.944 X 8.944 = 80,

2. -8.944 X -8.944 = 80,

so 8.944, or -8.944.

Question 4.

120

Answer:

10.9544 or -10.9544,

Explanation:

Given to find sqaure roots of 64

1. 10.9554 X 10.9554 = 120,

2. -10.9554X -10.9554 = 120,

so 10.9554, or -10.5994.

**Find the cube root of each number. Round your answer to the nearest tenth when you can.**

Question 5.

512

Answer:

8

Explanation:

Question 6.

1,000

Answer:

10

Explanation:

Question 7.

999

Answer:

9.997,

Explanation:

Question 8.

\(\frac{64}{343}\)

Answer:

\(\frac{4}{7}\),

Explanation:

As

So Cube root of \(\frac{64}{343}\) is \(\frac{4}{7}\).

Solve each equation involving a variable that ¡s squared.

Round your answer to the nearest tenth when you can.

Question 9.

a^{2} = 46.24

Answer:

a= 6.8,

Explanation:

Question 10.

b^{2} = \(\frac{25}{49}\)

Answer:

b= \(\frac{5}{7}\),

Explanation:

Given b^{2} = \(\frac{25}{49}\) as b^{2} = \(\frac{5X5}{7X7}\),

therefore b = square root of \(\frac{5X 5}{7 X 7}\) = \(\frac{5}{7}\),

Question 11.

m^{2} = 196

Answer:

m = 14,

Explanation:

Therefore m = 14.

Question 12.

n^{2} = 35o

Answer:

n= 18.708,

Explanation:

therefore n = 18.708.

**Solve each equation involving a variable that is cubed.
Write fractions in simplest form, and round decimal answers
to the nearest tenth.**

Question 13.

x^{3} = 74.088

Answer:

x =4.2,

Explanation:

the cube root of 74.088 is 4.2.

Question 14.

x^{3} = \(\frac{216}{729}\)

Answer:

x = \(\frac{6}{9}\),

Explanation:

the cube root of x^{3} = \(\frac{216}{729}\) so x = \(\frac{6}{9}\).

Question 15.

x^{3} = 1,728

Answer:

x= 12,

Explanation:

Question 16.

x^{3} = 2,500

Answer:

x= 13.572,

Explanation:

the cube root x = 13.572088083.

**Solve. Show your work. Round to the nearest tenth.**

Question 17.

The volume of a spherical tank is 790.272π cubic feet.

What is the diameter of the container?

Answer:

The diameter of the container is 16.8 ft,

Explanation:

Given the volume of a spherical tank is 790.272π cubic feet.

so radius is 4/3 pi r^{3} = 790.272π,

r^{3 }= (790.272 X 3)/4 = 592.704,

r= 8.4,

diameter of the container is 2r = 2 X 8.4 = 16.8 ft.

Question 18.

An orchard planted on a square plot of land has 3,136 apple trees.

If each tree requires an area of 4 square meters to grow,

find the length of each side of the plot of land.

Answer:

The length of each side of plot is 112 meters,

Explanation:

Given an orchard planted on a square plot of land has 3,136 apple trees.

If each tree requires an area of 4 square meters to grow,

the length of each side of the plot of land of square root of 3136 X 4

sqaure root of 12544 = 112 meters.

Question 19.

Mr. Berman deposited $2,500 in a savings account. Three years later there

was $2,812.16 in the savings account. Use the formula A = P(1 + r)^{n} to find

the rate of interest, r percent, that he was paid. A represents the final amount of the

investment, P is the original principal, and n is the number of years it was invested.

Answer:

Rate of intreset is 5.78%,

Explanation:

Given Mr. Berman deposited $2,500 in a savings account. Three years later there

was $2,812.16 in the savings account. Using the formula A = P(1 + r)^{n} to find

the rate of interest, r percent, that he was paid. A represents the final amount of the

investment, P is the original principal, and n is the number of years it was invested,

$2812.16 = $2,500(1 + r)^{3
}$2812.16 – $2,500 = (1 + r)^{3}** ^{
}**(1 + r)

^{3 }

**=**$312.16

**1 + r = cube root of $312.16,**

**1 + r = 6.7835,**

therefore r = 6.7835 – 1 = 5.7835.

Brain @ Work

Brain @ Work

Question 1.

Evaluate \(\frac{4^{3} \cdot 10^{4}}{5^{2}}\) without using a calculator.

Answer:

2^{10} X 5^{2},

Explanation:

Question 2.

Find the values of x and y that make the equation \(\frac{81 x^{4} \cdot 16 y^{4}}{\left[(2 y)^{2}\right]^{2}}\) = 1,296 true,

Answer:

X = 1.414 and y = 1,

Explanation:

Question 3.

Use each of the numbers 1 to 9 exactly once to fill in the blanks.

Answer:

3^{11},

Explanation:

Used each of the numbers 1 to 9 exactly once to fill the blanks

Question 4.

Jeremy wants to measure the radius of a marble. He uses a tank and

filled the tank with 360 identical marbles shown below, If the volume of the

tank is 9,720 cubic inches, find the radius of each marble.

Answer:

Radius is 3 inches,

Explanation:

Given Jeremy wants to measure the radius of a marble. He uses a tank and

filled the tank with 360 identical marbles shown below, If the volume of the

tank is 9,720 cubic inches, volume of each cube is 9,720 ÷ 360 = 27,

radius is cube root of 27 = 3 inches.