how to you simplify 5 sqrt 320 how do i start
320 = 4 * 4 * 4 * 5
The square root of each 4 is 2.
5√320 = 2*2*2*5√5 = 40√5
If you look up 320 or 5 on a square root table in the back of your statistics text you will get 17.8885 or 2.2361, respectively.
To simplify the expression 5√320, we can begin by finding the prime factorization of 320.
Step 1: Find the prime factors of 320.
320 can be written as 2 × 2 × 2 × 2 × 2 × 2 × 5 or 2^6 × 5.
Step 2: Group the prime factors in pairs, using the exponent as the index number.
Since there are six 2's, we can pair them up as 2^3 and leave one 2 unpaired. So, we have one pair of 2's and one unpaired 2, giving us 2^3 × 2 × 5.
Step 3: Simplify the expression.
Using multiplication properties, we can rewrite the expression as:
2^3 × 2 × 5 = 2^4 × 5
Step 4: Final answer.
Putting it all together, we have 5√320 = 5√(2^4 × 5) = 5 × 2^2√5 = 20√5.
Therefore, the simplified form of 5√320 is 20√5.
To simplify 5√320, you can follow these steps:
Step 1: Determine if there are any perfect square factors of the number underneath the square root sign (320 in this case).
Step 2: Divide 320 by the largest perfect square factor. In this case, 320 can be divided by 16, which is a perfect square:
320 ÷ 16 = 20
Step 3: Rewrite the square root expression with the perfect square factor outside the square root sign:
5√320 = 5√(16 * 20)
Step 4: Simplify the square root expression by separating the perfect square factor:
5√(16 * 20) = 5√16 * √20
Step 5: Simplify the perfect square factor outside the square root:
5√16 = 5 * 4 = 20
Step 6: Simplify the remaining square root by finding any perfect square factors. The remaining number, 20, can be divided by 4, which is another perfect square:
√20 = √(4 * 5) = 2√5
Step 7: Combine the simplified perfect square factor with the remaining square root:
5 * 20 = 100
So, 5√320 simplifies to 100√5.