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.
4=(sqrt2)4
[5sqrt(3)]/[2 - sqrt(3)] rationalize with the conjugate---- 2 + sqrt(3) ----- A polynomial expansion om bottom and distribution on top [5sqrt(3)]/[2 - sqrt(3)] * 2 + sqrt(3)/2 + sqrt(3) 10sqrt(3) + 5 * 3/2 - 3 - 10sqrt(3) + 15 ============
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).
square root of 20 = square root of 4 * square root of 5. square root of 4 = 2, so your answer is 2 square root of 5.
0.625
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.
Multiply everything by the square root of 3 minus the square root of 2 and then times that by 100 - 72 and divide that by 5
a+ square root of b has a conjugate a- square root of b and this is used rationalize the denominator when it contains a square root. If we want to multiply 5 x square root of 10 by something to get rid of the radical you can multiply it by square root of 10. But if we look at 5x( square root of 10 as ) 0+ 5x square root of 10 then the conjugate would be -5x square root of 10
4=(sqrt2)4
If you want to rationalize the denominator, then multiply numerator & denominator by sqrt(5), so 8*sqrt(5)/5 = approx 3.578
Yes. For example, the conjugate of (square root of 2 + square root of 3) is (square root of 2 - square root of 3).
-26
You rationalize denominators by using a form of one. Thus. sqrt(X + 6)/sqrt(X) * sqrt(X)/sqrt(X) = sqrt(X2 + 6X)/X ------------------------
1
[5sqrt(3)]/[2 - sqrt(3)] rationalize with the conjugate---- 2 + sqrt(3) ----- A polynomial expansion om bottom and distribution on top [5sqrt(3)]/[2 - sqrt(3)] * 2 + sqrt(3)/2 + sqrt(3) 10sqrt(3) + 5 * 3/2 - 3 - 10sqrt(3) + 15 ============
To simplify the square root of 5 times the square root of 6, you can multiply the two square roots together. This gives you the square root of (5*6), which simplifies to the square root of 30. Therefore, the simplified answer is the square root of 30.