Question
Simplify the expression
30z3−6
Evaluate
10z2×3z−6
Solution
More Steps

Evaluate
10z2×3z
Multiply the terms
30z2×z
Multiply the terms with the same base by adding their exponents
30z2+1
Add the numbers
30z3
30z3−6
Show Solution

Factor the expression
6(5z3−1)
Evaluate
10z2×3z−6
Multiply
More Steps

Evaluate
10z2×3z
Multiply the terms
30z2×z
Multiply the terms with the same base by adding their exponents
30z2+1
Add the numbers
30z3
30z3−6
Solution
6(5z3−1)
Show Solution

Find the roots
z=5325
Alternative Form
z≈0.584804
Evaluate
10z2×3z−6
To find the roots of the expression,set the expression equal to 0
10z2×3z−6=0
Multiply
More Steps

Multiply the terms
10z2×3z
Multiply the terms
30z2×z
Multiply the terms with the same base by adding their exponents
30z2+1
Add the numbers
30z3
30z3−6=0
Move the constant to the right-hand side and change its sign
30z3=0+6
Removing 0 doesn't change the value,so remove it from the expression
30z3=6
Divide both sides
3030z3=306
Divide the numbers
z3=306
Cancel out the common factor 6
z3=51
Take the 3-th root on both sides of the equation
3z3=351
Calculate
z=351
Solution
More Steps

Evaluate
351
To take a root of a fraction,take the root of the numerator and denominator separately
3531
Simplify the radical expression
351
Multiply by the Conjugate
35×352352
Simplify
35×352325
Multiply the numbers
More Steps

Evaluate
35×352
The product of roots with the same index is equal to the root of the product
35×52
Calculate the product
353
Reduce the index of the radical and exponent with 3
5
5325
z=5325
Alternative Form
z≈0.584804
Show Solution
