Surds as a single root and comparing
Move the number in front of the root under the root. Fill in the number under the root.
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Writing a surd as a single root is the opposite of simplifying it. We square the number in front of the square root and multiply the number under the root by it: 3√2 = √(9 · 2) = √18. This makes surds easy to compare — just compare the numbers under the roots.
What does this generator do?
On the easy level you move a number under a square root (5√3 = √75). On the medium level you move it under a cube root or a fourth root — then you cube the number or raise it to the power 4 (2∛5 = ∛40). On the hard level you compare two numbers, for example 2√7 and 3√3, or 3√5 and 7.
How to use it
1) Raise the number in front of the root to the power given by the index of the root (square it for √, cube it for ∛). 2) Multiply the number under the root by it. 3) To compare, rewrite both numbers as a single root and compare the numbers under them — a bigger number under the root means a bigger surd.