CheerMath

Grade 8 Squares, Square Roots & Radicals Practice

Reason with Perfect & Non-Perfect Square Roots

Go past the perfect squares! Work with bigger squares and roots, locate a root between two whole numbers, estimate non-perfect roots, and find square roots of fractions and decimals.

Also known as Class 8 maths — the same topics, whether your school calls it grade, class or year.

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Sample questions

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

  1. Locate Square Roots Between Whole Numbers

    Between which two consecutive whole numbers does 15\sqrt{15} lie?
    • 3 and 4
    • 2 and 3
    • 4 and 5
    • 5 and 6
    Show answer
    Answer:
    3 and 4

  2. Find Square Roots of Decimals

    What is the value of  0.25\sqrt{\,0.25}?
    • 0.05
    • 5
    • 0.5
    • 0.25
    Show answer
    Answer:
    0.5

  3. Strengthen Exact Squares & Square Roots

    □=12\sqrt{\square} = 12. What is the missing number?
    Show answer
    Answer:
    144

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A worked example

Between which two consecutive whole numbers does 15\sqrt{15} lie?
  1. We need to find the two consecutive whole numbers that 15\sqrt{15} lies between.
  2. The perfect squares near 15 are 9=32= 3^2 and 16=42= 4^2.
  3. Since 9<15<16, taking square roots of each part gives 3<15<43 < \sqrt{15} < 4.
  4. So 15\sqrt{15} lies between 3 and 4.

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