Question
Simplify the expression
−329r3−48
Evaluate
7r3−8r2×42r−48
Multiply
More Steps

Multiply the terms
−8r2×42r
Multiply the terms
−336r2×r
Multiply the terms with the same base by adding their exponents
−336r2+1
Add the numbers
−336r3
7r3−336r3−48
Solution
More Steps

Evaluate
7r3−336r3
Collect like terms by calculating the sum or difference of their coefficients
(7−336)r3
Subtract the numbers
−329r3
−329r3−48
Show Solution

Find the roots
r=−329236×3292
Alternative Form
r≈−0.526439
Evaluate
7r3−8r2×42r−48
To find the roots of the expression,set the expression equal to 0
7r3−8r2×42r−48=0
Multiply
More Steps

Multiply the terms
8r2×42r
Multiply the terms
336r2×r
Multiply the terms with the same base by adding their exponents
336r2+1
Add the numbers
336r3
7r3−336r3−48=0
Subtract the terms
More Steps

Simplify
7r3−336r3
Collect like terms by calculating the sum or difference of their coefficients
(7−336)r3
Subtract the numbers
−329r3
−329r3−48=0
Move the constant to the right-hand side and change its sign
−329r3=0+48
Removing 0 doesn't change the value,so remove it from the expression
−329r3=48
Change the signs on both sides of the equation
329r3=−48
Divide both sides
329329r3=329−48
Divide the numbers
r3=329−48
Use b−a=−ba=−ba to rewrite the fraction
r3=−32948
Take the 3-th root on both sides of the equation
3r3=3−32948
Calculate
r=3−32948
Solution
More Steps

Evaluate
3−32948
An odd root of a negative radicand is always a negative
−332948
To take a root of a fraction,take the root of the numerator and denominator separately
−3329348
Simplify the radical expression
More Steps

Evaluate
348
Write the expression as a product where the root of one of the factors can be evaluated
38×6
Write the number in exponential form with the base of 2
323×6
The root of a product is equal to the product of the roots of each factor
323×36
Reduce the index of the radical and exponent with 3
236
−3329236
Multiply by the Conjugate
3329×33292−236×33292
The product of roots with the same index is equal to the root of the product
3329×33292−236×3292
Multiply the numbers
More Steps

Evaluate
3329×33292
The product of roots with the same index is equal to the root of the product
3329×3292
Calculate the product
33293
Reduce the index of the radical and exponent with 3
329
329−236×3292
Calculate
−329236×3292
r=−329236×3292
Alternative Form
r≈−0.526439
Show Solution
