Math Simplification Calculator

Step-by-step solutions for radicals, exponents, binomials, and equations

Multiply Square Roots

Multiply square roots:

Coeff:

√

Coeff:

√

Result:

2√8 × 3√18

Step-by-Step Solution

Original: 2√8 × 3√18

Divide Square Roots

Divide square roots:

Coeff:

√

Coeff:

√

Result:

6√50 ÷ 2√2

Step-by-Step Solution

Original: 6√50 ÷ 2√2

Add/Subtract Square Roots

Add or subtract square roots:

Coeff:

√

Coeff:

√

Result:

3√12 + 2√27

Step-by-Step Solution

Original: 3√12 + 2√27

Simplify Exponents

Simplify exponent expression:

^{^}

Result:

2³ × 2⁴

Step-by-Step Solution

Original: 2³ × 2⁴

Multiply Binomials

Multiply binomials with radicals:

√

Result:

(2 + 3√5) × (1 + 2√5)

Step-by-Step Solution

Original: (2 + 3√5) × (1 + 2√5)

Solve Equations with Radicals

Solve equation √(ax + b) = c:

√(

x ) =

Solution:

x = ?

Step-by-Step Solution

Original: √(1x + 3) = 5

Mathematical Rules

√a × √b = √(a×b) and k√a × m√b = (k×m)√(a×b)

√a ÷ √b = √(a÷b) and k√a ÷ m√b = (k÷m)√(a÷b)

Like radicals (same radicand) can be added: k√a + m√a = (k+m)√a

Exponent multiplication: aᵐ × aⁿ = aᵐ⁺ⁿ

Exponent division: aᵐ ÷ aⁿ = aᵐ⁻ⁿ

Power of a power: (aᵐ)ⁿ = aᵐⁿ

FOIL: (a+b)(c+d) = ac + ad + bc + bd

To solve √(ax+b)=c: Square both sides → ax+b=c² → x=(c²-b)/a