Find the cube root of 512: ^3√512 .(1 point)
The cube root of 512 can be found by calculating the number that, when multiplied by itself three times, equals 512.
So, ^3√512 = 8.
To find the cube root of 512, you can use a calculator or mathematical techniques. Here's how you can do it manually:
1. Prime factorize the number. To prime factorize 512, divide it by the first prime number (2) repeatedly until you can't divide anymore:
512 ÷ 2 = 256
256 ÷ 2 = 128
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
Therefore, the prime factorization of 512 is 2^9.
2. Rewrite the number using exponents. Since the cube root is asking for the number that, when multiplied by itself three times, equals 512, you can rewrite 512 using exponents:
512 = (2^9) = 2^(9/3) = 2^3
Therefore, ∛512 = 2^3.
3. Simplify the exponent. Since 2 cubed (2^3) equals 8, the cube root of 512 is equal to 8.
Therefore, ∛512 = 8.
So, the cube root of 512 is 8.
To find the cube root of 512, we can use the formula:
^3√(x) = x^(1/3)
So, for 512, we have:
^3√(512) = 512^(1/3)
Calculating the value, we get:
^3√(512) = 8