Grade 9 Squares, Square Roots & Radicals Practice

Understand & Simplify Radicals

Meet the radical sign! Learn the parts of a radical, understand principal roots and the plus-or-minus sign, use prime factorization to simplify square roots, and work with cube roots.

Also known as Class 9 maths — the same topics, whether your school calls it grade, class or year.

Sample questions

A few samples from this topic — try one, then show the answer.

Simplify Square Roots

What is the simplified form of $\sqrt{\,48} \; + \; \sqrt{\,3}$ ?
- $\sqrt{\,51}$
- $3\sqrt{\,3}$
- $5\sqrt{\,3}$
- $4\sqrt{\,3}$
Show answer
Answer:
$5\sqrt{\,3}$
Understand Principal Square Roots & ±

Express both square roots of 64 using $\pm$ notation.
- $\pm64$
- 8
- -8
- $\pm8$
Show answer
Answer:
$\pm8$
Use Prime Factorization with Square Roots

Find the square root of a number whose prime factorization is $5^{4}$ .

Show answer
Answer:
25

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A worked example

What is the simplified form of

\sqrt{\,48} \; + \; \sqrt{\,3}

Simplify $\sqrt{\,48} \; + \; \sqrt{\,3}$ .
Find the largest perfect square factor of each radicand $\\ \sqrt{\,48} = \sqrt{16 \cdot 3} = 4\sqrt{\,3} \\ \sqrt{\,3}$ is already in simplest form
Combine like radicals $\to 4\sqrt{\,3} \; + \; \sqrt{\,3} = (4 + 1)\sqrt{\,3} = 5\sqrt{\,3}$
The simplified form is $5\sqrt{\,3}$ .

Skills covered

Read & Identify the Parts of a Radical
Understand Principal Square Roots & ±
Use Prime Factorization with Square Roots
Simplify Square Roots
Understand & Simplify Cube Roots
Convert Between Entire & Mixed Radicals
Recognize Equivalent Radical Forms
Evaluate Expressions Inside Radicals
Evaluate Expressions with Powers and Square Roots
Use Scientific Notation with Square Roots
Apply Square & Cube Roots in Problems

Squares, Square Roots & Radicals in other grades

Grade 8: Reason with Perfect & Non-Perfect Square Roots

For parents & teachers

Your child learns radical notation properly — the radical sign, index and radicand, the principal root and when a plus-or-minus answer is needed — then simplifies square roots using prime factorization, converts between entire and mixed radicals, and meets cube roots and radicals in scientific notation.

Understanding and simplifying radicals: reviewing exact, estimated, fraction and decimal square roots, reading and identifying the parts of a radical, understanding principal square roots and plus-or-minus answers, using prime factorization with square roots, simplifying square roots, understanding and simplifying cube roots, converting between entire and mixed radicals, recognizing equivalent radical forms, evaluating expressions inside radicals, evaluating expressions with powers and square roots, using scientific notation with square roots, and applying square and cube roots in problems.

Grade 9 Squares, Square Roots & Radicals Practice

Sample questions

A worked example

More Grade 9 topics