simplify by factoring
sqrt1575to the 4th
sorry not sure how to type it out right
(√1575)^4
= (1575^(1/2))^4
= 1575^2 = 2480625
1575=3*3*5*5*7=3^2*5^2*7
sqroot(1575)=sqroot(3^2*5^2*7)
=3*5*sqroot(7)=15*sqroot(7)
sqroot(1575)=15*sqroot(7)
To simplify the expression sqrt(1575) to the 4th power by factoring, we need to break down 1575 into its prime factors.
First, let's find the prime factorization of 1575:
We start by dividing 1575 by the smallest prime number, 2, repeatedly until we can no longer divide evenly:
1575 ÷ 2 = 787.5 (not divisible by 2)
Next, we try dividing by the next prime number, 3:
787.5 ÷ 3 = 262.5 (not divisible by 3)
Then, we try dividing by 5:
262.5 ÷ 5 = 52.5 (not divisible by 5)
Continuing, we try dividing by 7:
52.5 ÷ 7 = 7.5 (not divisible by 7)
Finally, we try dividing by 3 again:
7.5 ÷ 3 = 2.5 (not divisible by 3)
We can see that we can't divide 2.5 any further by prime numbers. So the prime factorization of 1575 is:
1575 = 3 x 3 x 5 x 5 x 7
Now, let's simplify the expression sqrt(1575)^4:
(sqrt(1575))^4 = (3 x 3 x 5 x 5 x 7)^4
Since we're raising a square root to the 4th power, we can eliminate the square root sign:
(3 x 3 x 5 x 5 x 7)^4 = (3^2 x 5^2 x 7)^4
Simplifying the exponents:
(3^2 x 5^2 x 7)^4 = 3^8 x 5^4 x 7^4
So the simplified expression is:
sqrt(1575)^4 = 3^8 x 5^4 x 7^4