Grade 9 · Algebra & functions

Simplifying square roots (ACT) practice

Simplifying square roots (ACT) is a grade 9 math skill aligned to Common Core standard HSN.RN.A.2: rewrite expressions involving radicals and rational exponents using the properties of exponents. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 simplifying square roots (act) problems our math games drill.

CCSS HSN.RN.A.210 questions in the bank

Sample questions

Try 8 for free

Question 1easy

Which expression is equivalent to $\sqrt{720}$ ?

$720 = 144 \cdot 5$ , so $\sqrt{720} = \sqrt{144 \cdot 5} = 12\sqrt{5}$ .

Question 2easy

Which expression is equivalent to $\sqrt{192}$ ?

$192 = 64 \cdot 3$ , so $\sqrt{192} = \sqrt{64 \cdot 3} = 8\sqrt{3}$ .

Question 3easy

Which expression is equivalent to $\sqrt{288}$ ?

$288 = 144 \cdot 2$ , so $\sqrt{288} = \sqrt{144 \cdot 2} = 12\sqrt{2}$ .

Question 4easy

Which expression is equivalent to $\sqrt{750}$ ?

$750 = 25 \cdot 30$ , so $\sqrt{750} = \sqrt{25 \cdot 30} = 5\sqrt{30}$ , and $30 = 2 \cdot 3 \cdot 5$ is square-free.

Question 5medium

Which expression is equivalent to $\sqrt{5400}$ ?

$5400 = 900 \cdot 6$ , so $\sqrt{5400} = \sqrt{900 \cdot 6} = 30\sqrt{6}$ .

Question 6medium

Which expression is equivalent to $\sqrt{8820}$ ?

$8820 = 36 \cdot 245 = 36 \cdot 49 \cdot 5 = 1764 \cdot 5$ , so $\sqrt{8820} = 42\sqrt{5}$ .

Question 7medium

Which expression is equivalent to $\sqrt{4050}$ ?

$4050 = 45^2 \cdot 2$ , so $\sqrt{4050} = 45\sqrt{2}$ .

Question 8medium

Which expression is equivalent to $\sqrt{9800}$ ?

$9800 = 70^2 \cdot 2$ , so $\sqrt{9800} = 70\sqrt{2}$ .

Tests that cover simplifying square roots (act):

NAEP SAT SBAC NC EOG/EOC VTCAP

More Grade 9 skills:

Scalar times 2×2 matrix (ACT)Slope-intercept intercepts Rational exponents Slope-point line equations Rational equation solving (SAT)Square and cube binomials Radical word problems (ACT)Systems of equations All Grade 9 practice →

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