Simplify
A.1/root a +2
b.root 18/25
c.root a x cubed root a
d.root x + 2 root y/root x-2 root y
e.root5 x root72 /root 3
you really have to use brackets to establish the order of operations you want.
e.g. in #1,
the way you typed it it would be (1/√a) + 2
but I sense you meant 1/(√a + 2)
in b) did you mean √(18/25) ?
etc
e) is the only one not ambiguous,
√5*(√72/√3)
= √5*√24
= √120
= 2√30
Also your use of x is not consistent
in c) you are using x as a multiplier, in d) you are using x as a variable
if you have to show a multiplication signs, either use brackets such as (2)(3) or the * sign,
eg 2*3
Key
*=multiplication
|= square root because I don't have the correct symbol
A.1/|a +2
b.|18/25
c.|a * 3|a
d.|x + 2|y / |x - 2|y
Please help
Ok, so you are saying
a. 1/√a + 2
= (1/√a)(√a/√a) + 2
= (√a)/a + 2
b. still not clear if you meant
√(18/25) or √18 /25
for first interpretation: = 3√2/5
for 2nd interpretation: = 3√2 /25
c). I will take the original as
squareroot(a) * cuberoot(a)
= a^(1/2) * a^(1/3)
= a^(1/2+1/3)
= a^(5/6) or (sixthroot(a))^5
d) again, I will read it as
y√(x+2)/(y√(x-2) )
= √(x+2)/√(x-2)
= √(x+2)/√(x-2) * √(x-2)/√(x-2)
= √((x+2)(x-2) )/(x-2)
= √(x^2 - 4)/(x-2)
the second line of √(x+2)/√(x-2) should be accepted as simplified as well, unless it wanted the denominator rationalized
Thanks alot reiny
To simplify each of the expressions, we need to simplify the square roots and reduce any fractions.
A.
To simplify 1/√a + 2, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of √a is √a. So, we multiply numerator and denominator by √a.
[(1/√a + 2) x (√a/√a)] / (√a/√a)
= (√a + 2√a) / √a
= (3√a) / √a
= 3
Therefore, the simplified expression is 3.
B.
To simplify √(18/25), we first simplify the numerator and denominator separately:
√18 = √(9 x 2) = 3√2
√25 = 5
So the expression becomes (√18/√25) = (3√2/5)
Therefore, the simplified expression is 3√2/5.
C.
To simplify √a x ∛a, we can combine the square root and cube root by multiplying the exponents together.
a^(1/2) x a^(1/3) = a^(1/2 + 1/3) = a^(5/6)
Therefore, the simplified expression is √a x ∛a = a^(5/6).
D.
To simplify √x + 2√y / √x - 2√y, we need to rationalize the denominator. This involves multiplying both the numerator and denominator by the conjugate of the denominator, which is √x + 2√y.
[(√x + 2√y)(√x + 2√y) / (√x - 2√y)(√x + 2√y)]
Using the FOIL method in the numerator:
= (√x)(√x) + (√x)(2√y) + (2√y)(√x) + (2√y)(2√y)
= x + 2√xy + 2√xy + 4y
= x + 4√xy + 4y
Using the FOIL method in the denominator:
= (√x)(√x) + (√x)(2√y) - (2√y)(√x) - (2√y)(2√y)
= x + 2√xy - 2√xy - 4y
= x - 4y
Therefore, the expression simplifies to (x + 4√xy + 4y) / (x - 4y).
E.
To simplify √(5x) * √72 / √3, we can simplify each square root and combine them together:
√(5x) = √5 * √x
√72 = √(9 * 8) = √9 * √8 = 3√8
√3 remains unchanged
The expression becomes (√5 * √x) * (3√8) / √3
Multiplying the square root terms:
√5 * √x * 3√8 = 3√(5x * 8) = 3√(40x)
The expression becomes 3√(40x) / √3
To simplify further, we can rationalize the denominator by multiplying both numerator and denominator by √3:
(3√(40x) / √3) * (√3 / √3) = 3√(120x) / 3
Simplifying the numerator:
3√(120x) = 3√(12 * 10 * x) = 3√(12) * √(10) * √(x) = 6√(10x)
The expression simplifies to 6√(10x) / 3
Finally, dividing both numerator and denominator by 3:
(6√(10x) / 3) / (3 / 3) = 6√(10x)
Therefore, the simplified expression is 6√(10x).