Square Roots and Cube Roots

​SQUARE ROOTS AND CUBE ROOTS

​Three expressions with exponents are given below. For each expression, label the base and the exponent.
Then, explain its mathematical meaning by writing it in expanded form.

​Similar to the inverse operations of addition and subtraction, raising a value to an exponent also has an inverse operation. Use the table below to explore one example.

​SQUARES AND SQUARE ROOTS

​• Squaring a number is raising that number to a power of 2 or multiplying a number by itself.

• The square root is an inverse operation of squaring a number and “undoes” an exponent of 2.

• The positive square root is known as the principle square root.

​The square root of x:

√X

“What number times itself will give me x?”

​In 1-4, use squares and square roots to evaluate the given expression.

​5. Three equations are given below. Use inverse operations to isolate the variable. Be sure to check your solution by plugging it back into the original equation.

Math Response

1. 1. $$15^2$$

Type answer here

Correct Answer: 225

Deg^°

Rad

Math Response

2. 2. $$\sqrt[]{144}$$

Type answer here

Correct Answer: 12

Deg^°

Rad

Math Response

3. $$\left(-6\right)^2$$

Type answer here

Correct Answer: 36

Deg^°

Rad

Math Response

4. $$\sqrt[]{49}$$

Type answer here

Correct Answer: 7

Deg^°

Rad

A similar relationship between squares and square roots exists between cubes and cube roots.

​CUBES
AND

CUBE

ROOTS

• Cubing a number is raising that number to a power of _____ or multiplying it by itself three times.

• The cube root is an ________________ operation of cubing a number and “undoes” an exponent of 3.

​In 1-4, use squares and square roots to evaluate the given expression.

​5. Three equations are given below. Use inverse operations to isolate the variable. Be sure to check your solution by plugging it back into the original equation.

​Complete the table as a reference for the first ten perfect cubes.

13​	23	33	43	53
​	​	​	​	​

63	73	83	93	103
​	​	​	​	​

Match

Match the following

• 1

• 27

• 125

• 343

• 729

• $$1^3$$

• $$3^3$$

• $$5^3$$

• $$7^3$$

• $$9^3$$

Match

Match the Following

• 8
• 64
• 216
• 512
• 1000

• $$2^3$$

• $$4^3$$

• $$6^3$$

• $$8^3$$

• $$10^3$$