0580 · Notes & worked examples
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Write \(\displaystyle \sqrt{75}\) as \(\displaystyle k\sqrt{3}\). Find k.
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Write \(\displaystyle \sqrt{180}\) as \(\displaystyle k\sqrt{5}\). Find k.
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Find the coefficient of \(\displaystyle \sqrt{5}\) in \(\displaystyle 6\sqrt{5}+4\sqrt{5}\).
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Find the coefficient of \(\displaystyle \sqrt{6}\) in \(\displaystyle 7\sqrt{6}+5\sqrt{6}\).
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Find \(\displaystyle \sqrt{294} \times \sqrt{150}\).
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Find \(\displaystyle \sqrt{128} \times \sqrt{72}\).
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Find the coefficient of \(\displaystyle \sqrt{2}\) in \(\displaystyle 8\sqrt{2}-6\sqrt{2}\).
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
Maths4U Original · Short practice
Keep all values exact. Each square root denotes its nonnegative real value.
Find the coefficient of \(\displaystyle \sqrt{3}\) in \(\displaystyle 2\sqrt{3}-7\sqrt{3}\).
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.