Solving x² = p and x³ = p
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Solving x² = p and x³ = p
Solving x² = p and x³ = p worksheet for Grade 8: twelve equations, such as x² = 49 (x = 7 or −7), x² = 7 (√7 or −√7) and x³ = −27 (x = −3), with fractions too. With an answer key.
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Teach it first
Solving x² = p and x³ = pA teaching handout to hand out before this sheet: the rule, worked examples and common mistakes.- Pages
- 1
- Last updated
- Time
- About 15 minutes
- Answer key
- Included
- Printing
- Black and white
- Related curriculum
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Find square roots of perfect squares and cube roots of perfect cubes, solve x² = p and x³ = p, and say which two whole numbers a square root is between.
Reviewed by Mr. Robert Harrison, Teacher. How we check worksheets
How to use this sheet
- Keep a list of the perfect squares to 144 and the perfect cubes to 125 beside the sheet.
- For estimating, have the child find the two perfect squares the number is between first.
- Ask the child to check each root by multiplying it back.
Common mistakes
- Dividing by 2 for a square root, so the square root of 16 becomes 8. Ask which number times itself makes 16.
- Thinking every square root is irrational. The square root of 49 is 7, a whole number.
- Thinking a repeating decimal is irrational. Repeating decimals are fractions, so they are rational.
