The idea is to get rid of the square root in the denominator. For this purpose, you must multiply numerator and denominator by the square root of 6 in this case.
Yes. For example, the conjugate of (square root of 2 + square root of 3) is (square root of 2 - square root of 3).
Multiplicative inverse is the number that, when multiplied, results in 1, usually 1/# 1/sqrt7 is the inverse, so just rationalize the denominator sqrt7/7 = square root of 7 divided by 7
Yes. The original denominator and its conjugate will form the factors of a Difference of Two Squares (DOTS) and that will rationalise the denominator but only if the radicals are SQUARE roots.
If you want to rationalize the denominator, then multiply numerator & denominator by sqrt(5), so 8*sqrt(5)/5 = approx 3.578
In a way. You can multiply top and bottom by the square root of 2. This will not exactly make the expression simpler, but you'll get rid of the square root in the denominator (and transfer it to the numerator); this is considered to be the standard form for expressions which involve square roots. In other words, there should be no square roots in the denominator.
8/sqrt(2) to get exact answer rationalize the denominator by this form of 1 sqrt(2)/sqrt(2) * 8/sqrt(2) = 8*sqrt(2)/2 or, the decimal answer = 5.656854249
5/(√3 - 1)= 5(√3 + 1)/(√3 - 1)(√3 + 1)= (5√3 + 5)/[(√3)2 - 12)= (5√3 + 5)/(3 - 1)= 5√3 + 5)/2= 5√3/2 + 1/2
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).
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).
It is the square of the numerator divided by the square of the denominator. Thus, for example, square(2/3) = square(2)/square(3) = 4/9
It is easier to describe using an actual example. Say you have an expression x/sqrt(2). Then multiply by sqrt(2)/sqrt(2) (which is of course equal to 1 and we know that anything multiplied by 1 stays the same. This will get rid of the radical on the bottom. So the expression becomes x/sqrt(2) * sqrt(2)/sqrt(2) = [x*sqrt(2)]/2 where * means multiply
(2√24) / √54 = (2√4√6) / (√9√6) = (4√6)/(3√6) = 4/3
It looks like your question is [1-sqrt(3)] / [1+sqrt(3)], and you want to rationalize the denominator. If this is the case, multiply both numerator and denominator by (1-sqrt(3)), and get for the denominator = -2, and the numerator = 4 - 2*sqrt(3), so the answer is sqrt(3) - 2
You cannot. The square root of 5 is irrational.