rationalise 5+2square root 5 divided by square root 5.
please can someone help me on how to get the answer 2+square root 5
(5+2sqrt5)/sqrt5 * (sqrt5/sqrt5)=
(2*sqrt5*sqrt5+5sqrt5)/(sqrt5*sqrt5)=
(2*5+5sqrt5)/5=2+sqrt5
but how do you get 2*5+5squared root 5 to become 2+sqrt5 ?
To rationalize the expression (5 + 2√5) / √5, we need to eliminate the square root in the denominator.
To do this, we multiply both the numerator and the denominator by the conjugate of the denominator, which is √5.
(5 + 2√5) / √5 * (√5 / √5)
To simplify, we multiply the numerators and the denominators:
(5 * √5 + 2√5 * √5) / (√5 * √5)
Simplifying further:
(5√5 + 2√(5 * 5)) / 5
(5√5 + 2√25) / 5
(5√5 + 2 * 5) / 5
(5√5 + 10) / 5
Now, we can divide each term by 5:
5√5 / 5 + 10 / 5
√5 + 2
So the final simplified expression is 2 + √5.
To rationalize the expression (5 + 2√5) / √5, we need to eliminate the radical in the denominator. Here's how you can do it:
Step 1: Multiply the numerator and denominator by the conjugate of the denominator. The conjugate of √5 is -√5, so we multiply both the numerator and denominator by (-√5):
(5 + 2√5) / √5 * (-√5) / (-√5)
Step 2: Simplify the expression:
((-√5)(5) + (-√5)(2√5)) / ((-√5)(√5))
(-5√5 - 2√5) / (-√5 * √5)
(-5√5 - 2√5) / (-√5 * √5) simplifies to:
(-7√5) / -5
Step 3: Simplify further by canceling out the negative signs:
(-7√5) / -5 = 7√5 / 5
So, the final result is 7√5 / 5.