5 third root 48 - third root 750
5 * (thirdrt 48) - (thirdrt 750)
breakdown the radicals
5 * (3rt 8)(3rt 6) - (3rt 125)(3rt 6)
can you do this now?
would it be 5 third root 6?
yes, correct
good job! :)
To solve the equation "5√48 - ∛750", we need to evaluate the individual square root and cube root expressions and then subtract them.
Step 1: Evaluate the square root of 48.
To find the square root of 48, we need to determine a number that, when multiplied by itself, equals 48. We can approximate this value by using a calculator or by using a prime factorization method.
Prime factorization of 48:
48 = 2 × 2 × 2 × 2 × 3
Since there are two pairs of 2's, we can take one 2 from each pair out and simplify the square root expression.
√48 = √(2 × 2 × 2 × 2 × 3)
= 2 × 2 × √3
= 4√3
Step 2: Evaluate the cube root of 750.
To find the cube root of 750, we need to determine a number that, when multiplied by itself twice, equals 750. Again, we can approximate this value by using a calculator or by estimating.
Since 8 x 8 x 8 = 512 and 9 x 9 x 9 = 729, the cube root of 750 will be between 8 and 9. Let's assume it's closer to 8 for simplicity.
∛750 ≈ ∛(8 × 8 × 8 × 1.22)
≈ 8 × 1.22
≈ 9.76
Step 3: Subtract the cube root from the square root.
Substituting the above values into the original expression, we get:
5√48 - ∛750
= 5(4√3) - 9.76
Now, multiply the coefficient 5 by the square root expression:
= 20√3 - 9.76
The resulting expression cannot be simplified further as the square root of 3 and the number 9.76 are not like terms.
Therefore, the final answer for the expression "5√48 - ∛750" is "20√3 - 9.76".