Question
Simplify the expression
23d4−100
Evaluate
d×d3×23−100
Solution
More Steps

Evaluate
d×d3×23
Multiply the terms with the same base by adding their exponents
d1+3×23
Add the numbers
d4×23
Use the commutative property to reorder the terms
23d4
23d4−100
Show Solution

Find the roots
d1=−2341216700,d2=2341216700
Alternative Form
d1≈−1.444003,d2≈1.444003
Evaluate
d×d3×23−100
To find the roots of the expression,set the expression equal to 0
d×d3×23−100=0
Multiply
More Steps

Multiply the terms
d×d3×23
Multiply the terms with the same base by adding their exponents
d1+3×23
Add the numbers
d4×23
Use the commutative property to reorder the terms
23d4
23d4−100=0
Move the constant to the right-hand side and change its sign
23d4=0+100
Removing 0 doesn't change the value,so remove it from the expression
23d4=100
Divide both sides
2323d4=23100
Divide the numbers
d4=23100
Take the root of both sides of the equation and remember to use both positive and negative roots
d=±423100
Simplify the expression
More Steps

Evaluate
423100
To take a root of a fraction,take the root of the numerator and denominator separately
4234100
Simplify the radical expression
42310
Multiply by the Conjugate
423×423310×4233
Simplify
423×423310×412167
Multiply the numbers
More Steps

Evaluate
10×412167
Use na=mnam to expand the expression
4102×412167
The product of roots with the same index is equal to the root of the product
4102×12167
Calculate the product
41216700
423×423341216700
Multiply the numbers
More Steps

Evaluate
423×4233
The product of roots with the same index is equal to the root of the product
423×233
Calculate the product
4234
Reduce the index of the radical and exponent with 4
23
2341216700
d=±2341216700
Separate the equation into 2 possible cases
d=2341216700d=−2341216700
Solution
d1=−2341216700,d2=2341216700
Alternative Form
d1≈−1.444003,d2≈1.444003
Show Solution
