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".