Squares, cubes and numerical roots · Short practice

Check a final answer, then explain the reasoning on paper. Guest progress stays in this browser; an account saves future checks without overwriting your first result.

Recall

Squares, cubes and numerical roots — objective 1

Maths4U Original · Short practice

Let \(\displaystyle a=10\) and \(\displaystyle b=7\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle a^{2}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Squares, cubes and numerical roots — objective 1

Maths4U Original · Short practice

Let \(\displaystyle a=11\) and \(\displaystyle b=2\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle a^{2}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Method

Squares, cubes and numerical roots — objective 2

Maths4U Original · Short practice

Let \(\displaystyle a=11\) and \(\displaystyle b=2\). Apply the stated brackets and root conventions.

Calculate the principal square root of 121.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Squares, cubes and numerical roots — objective 2

Maths4U Original · Short practice

Let \(\displaystyle a=12\) and \(\displaystyle b=3\). Apply the stated brackets and root conventions.

Calculate the principal square root of 144.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Apply

Squares, cubes and numerical roots — objective 3

Maths4U Original · Short practice

Let \(\displaystyle a=12\) and \(\displaystyle b=3\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle (-b)^{3}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Squares, cubes and numerical roots — objective 3

Maths4U Original · Short practice

Let \(\displaystyle a=3\) and \(\displaystyle b=4\). Apply the stated brackets and root conventions.

Calculate \(\displaystyle (-b)^{3}\).

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Check understanding

Squares, cubes and numerical roots — objective 4

Maths4U Original · Short practice

Let \(\displaystyle a=3\) and \(\displaystyle b=4\). Apply the stated brackets and root conventions.

Calculate the real cube root of -64.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

Fresh review variant

Squares, cubes and numerical roots — objective 4

Maths4U Original · Short practice

Let \(\displaystyle a=4\) and \(\displaystyle b=5\). Apply the stated brackets and root conventions.

Calculate the real cube root of -125.

Enter one exact number or fraction unless the question specifies rounding. If it asks for a coefficient of π, enter that coefficient only. Give full reasoning separately for written problems.

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