Irrational number approximations. Game on.

Irrational number approximations is a grade 8 math skill aligned to Common Core standard 8.NS.A.2: use rational approximations of irrational numbers to compare their size and locate them approximately on a number line diagram. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 20 irrational number approximations problems our math games drill.

CCSS 8.NS.A.220 questions in the bank

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Warm-upeasy

$\sqrt{27}$ lies between two consecutive integers. Enter the larger one.

$5^2 = 25 < 27 < 36 = 6^2$ , so $\sqrt{27}$ is between $5$ and $6$ ; the larger is $6$ .

Mid-gameeasy

What integer is closest to $\sqrt{120}$ ?

$11^2 = 121$ sits right above $120$ and $\sqrt{120} \approx 10.95$ , so the closest integer is $11$ .

Mid-gameeasy

What is the integer part of $\sqrt{10} + 2$ ?

$\sqrt{10} \approx 3.16$ , so $\sqrt{10} + 2 \approx 5.16$ ; the integer part is $5$ .

Mid-gameeasy

Which is closest to $\pi$ ?

$\pi \approx 3.14159$ .

Mid-gameeasy

Which is closest to $\sqrt{2}$ ?

$\sqrt{2} \approx 1.414$ .

Mid-gameeasy

Which is closest to $\sqrt{3}$ ?

$\sqrt{3} \approx 1.732$ .

Mid-gameeasy

Which is closest to $\sqrt{5}$ ?

$\sqrt{5} \approx 2.236$ .

Buzzer beatereasy

$\sqrt{40}$ is between two consecutive integers. Enter the smaller one.

$6^2 = 36 < 40 < 49 = 7^2$ , so $\sqrt{40}$ is between $6$ and $7$ ; the smaller is $6$ .

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