yes, it is root 9
* * * * *
which, is 3.
General rule: root(x) * root(x) = x
Normally, surds take their principal values, but if you want to be pedantic about it,
root(x) * root(x) = ± x.
Chat with our AI personalities
An example may help. If you have the fraction 1 / (2 + root(3)), where root() is the square root function, you multiply top and bottom by (2 - root(3)). If you multiply everything out, you will have no square root in the denominator, instead, you will have a square root in the numerator. If the denominator is only a root, eg root(3), you multiply top and bottom by root(3).
81
Depends on the situation. You usually have to multiply numerator and denominator by some number or expression. Examples: 1 / square root of 2 Here, you have to multiply numerator and denominator by the square root of 2. 1 / (square root of 2 + square root of 3) Here, you have to multiply numerator and denominator by (square root of 2 - square root of 3).
3
To multiply 2 square root of 2 by 3 square root of 6, simplify each square root separately first: 2 square root of 2 simplifies to 2√2, and 3 square root of 6 simplifies to 3√6. Then, multiply the coefficients (2 and 3) to get 6, and multiply the square roots (√2 and √6) to get √(2x6) = √12. So, the final answer is 6√12.