Square Roots and Cube Roots

Math ⇒ Number and Operations

Square Roots and Cube Roots starts at 7 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Square Roots and Cube Roots. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 10

Explain the difference between a square root and a cube root.

Explain why every positive real number has two square roots.

Explain why the square root of a negative number is not a real number.

If a number has a cube root of 9, what is the number?

If a number has a square root of 12, what is the number?

If x = √81, what is the value of x?

If x² = 49, what are the possible values of x?

If y³ = 125, what is the value of y?

What is the principal square root of 121?

What is the value of (√16) + (³√27)?

What is the value of √(100) - ³√(27)?

What is the value of √(2² + 3²)?

What is the value of √(49) + ³√(8)?

What is the value of ³√(1000) + √(49)?

Given that √x + √y = 10 and x + y = 34, where x and y are positive integers, find the values of x and y.

If √(x) = 7, what is the value of √(4x)?

If a number is both a perfect square and a perfect cube, what is the least such positive integer greater than 1?

If x = 2√3 and y = 3√2, find the value of x² + y².

Prove that the square root of any non-square natural number is irrational.

Simplify the expression: √(50) + 2√(8) - √(18). Give your answer in simplest radical form.