Multiplying and dividing surds
Work it out and simplify the answer.
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Roots with the same index are multiplied by multiplying the numbers under them: √2 · √8 = √16 = 4. When dividing, we divide the numbers under the roots. With brackets we work as with expressions — expand them or use the identities (a + b)(a − b) = a² − b² and (a + b)² = a² + 2ab + b².
What does this generator do?
On the easy level you multiply and divide two surds (√10 · √2, √80 ÷ √5). On the medium level you multiply surds with numbers in front of them and expand the bracket √5 · (√20 − 3). On the hard level you use the identities: (√3 + 5)(√3 − 5), (√2 + √3)² or (2 + √3)(1 − √3).
How to use it
1) Multiply the numbers in front of the roots, and separately the numbers under the roots. 2) Simplify the answer. 3) If you get a number without a root and a surd, write them into the boxes of the form p + q√r. Write a negative coefficient with a minus sign.