Simplify 4sqrt6/ sqrt30 by rationalizing the denominator.
Need help can someone show me steps on how to do this
To simplify and rationalize the denominator of the expression 4√6/√30, you need to eliminate the radical from the denominator.
Here are the steps to follow:
Step 1: Simplify the radicals in the numerator and denominator.
4√6 = √16 * √6 = 2√6
√30 remains as is.
Step 2: Simplify the denominator.
√30 = √(2 * 3 * 5) = √2 * √3 * √5 = √2√3√5 = √2√15
Step 3: Rewrite the expression with the simplified radicals.
4√6/√30 = (2√6) / (√2√15)
Step 4: Multiply the numerator and denominator by the conjugate of the denominator. The conjugate is obtained by changing the sign between the terms involving the radical, which in this case would be (√2√15).
(2√6) / (√2√15) * (√2√15) / (√2√15) = (2√6)(√2√15) / (√2√15)(√2√15)
Step 5: Simplify and eliminate the radicals as much as possible:
(2√6)(√2√15) = 2√6√2√15 = 2√12√15
(√2√15)(√2√15) = (√2√15)^2 = 2√15 * √15 = 2√225 = 2 * 15 = 30
Step 6: Simplify the expression further:
2√12√15 / 30 = (2√(4 * 3) * √15) / 30 = (2 * 2√3 * √15) / 30 = 4√3√15 / 30
Step 7: Simplify the expression and reduce it to the lowest terms, if possible:
4√3√15 / 30 = (4 * √3 * √15) / 30 = (4√45) / 30 = (4 * √(9 * 5)) / 30 = (4 * 3√5) / 30 = 12√5 / 30
Finally, the fully simplified and rationalized form of 4√6/√30 is 12√5/30.
Note: If you further simplify the expression by dividing both the numerator and denominator by their greatest common factor (GCF) of 6, you will get 2√5 / 5 as the simplest form.
multiply by sqrt30/sqrt30
you now have 4sqrt6*sqrt30/30
but sqrt 30=sqrt(5*6)=sqrt5*sqrt6
now you have 4sqrt6*sqrt6*sqrt5/30=24*sqrt5/30=.8 sqrt5