Which two integers is root(3) 22 between? Choices: [[1 and 2][15 and 16][16 and 17][2 and 3]]

Find Perfect Cubes: Find the perfect cubes that are just below and just above 22. The perfect cube just below 22 is 8 (since 2^3 = 8). The perfect cube just above 22 is 27 (since 3^3 = 27).Calculate Cube Root of 8: Calculate the cube root of 8. 2 * 2 * 2 = 8 2^3 = 8 The cube root of 8 is 2.Calculate Cube Root of 27: Calculate the cube root of 27. 3 * 3 * 3 = 27 3^3 = 27 The cube root of 27 is 3.Determine Cube Root of 22: Determine between which two integers the cube root of 22 falls. Since the cube root of 8 is 2 and the cube root of 27 is 3, we can conclude that: 2 < cube root of 22 < 3 Therefore, the cube root of 22 falls between the integers 2 and 3.

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Math Problems

Grade 8

Estimate cube roots

Full solution

Q. Which two integers is

\sqrt[3]{22}

between?

\newline

Choices:

\newline

(A)

[1 \text{ and } 2]

\newline

(B)

[15 \text{ and } 16]

\newline

(C)

[16 \text{ and } 17]

\newline

(D)

[2 \text{ and } 3]

Find Perfect Cubes: Find the perfect cubes that are just below and just above $22$ . $\newline$ The perfect cube just below $22$ is $8$ (since $2^3 = 8$ ). $\newline$ The perfect cube just above $22$ is $27$ (since $3^3 = 27$ ).
Calculate Cube Root of $8$ : Calculate the cube root of $8$ . $\newline$ $2 \times 2 \times 2 = 8$ $\newline$ $2^3 = 8$ $\newline$ The cube root of $8$ is $2$ .
Calculate Cube Root of $27$ : Calculate the cube root of $27$ . $\newline$ $3 \times 3 \times 3 = 27$ $\newline$ $3^3 = 27$ $\newline$ The cube root of $27$ is $3$ .
Determine Cube Root of $22$ : Determine between which two integers the cube root of $22$ falls. $\newline$ Since the cube root of $8$ is $2$ and the cube root of $27$ is $3$ , we can conclude that: $\newline$ 2 < \sqrt[3]{22} < 3 $\newline$ Therefore, the cube root of $22$ falls between the integers $2$ and $3$ .