Advanced Roots & Binomials Calculator

With Step-by-Step Solutions for Grade 8+ Mathematics.

Multiply Square Roots

Coeff:
√
×
Coeff:
√
Multiplication Result:
-
Multiplication Rule:
√a × √b = √(a × b)
k√a × m√b =
(k × m)√(a × b)
Step-by-Step Solution:
Enter square roots to see solution steps

Divide Square Roots

Coeff:
√
÷
Coeff:
√
Division Result:
-
Division Rule:
√a ÷ √b = √(a ÷ b)
k√a ÷ m√b =
(k ÷ m)√(a ÷ b)
Step-by-Step Solution:
Enter square roots to see solution steps

Add/Subtract Square Roots

Coeff:
√
Coeff:
√
Addition/Subtraction Result:
-
Addition/Subtraction Rule:
k√a + m√a = (k + m)√a
k√a - m√a = (k - m)√a
Only like radicals can be combined!
Step-by-Step Solution:
Enter square roots to see solution steps

Multiply Binomials

√
×
√
Binomial Multiplication Result:
-
FOIL Method:
(a ± b√c)(d ± e√f) =
a×d ± a×e√f ± b√c×d + b√c×e√f
= ad ± ae√f ± bd√c + be√(cf)
Step-by-Step Solution:
Enter binomials to see solution steps

Divide Binomials

√
÷
√
Binomial Division Result:
-
Division Method:
(a ± b√c) ÷ (d ± e√f) =
Multiply numerator & denominator by conjugate:
(a ± b√c)(d ∓ e√f) ÷ (d² - e²f)
Step-by-Step Solution:
Enter binomials to see solution steps
Rules for Working with Radicals & Binomials
√(a × b) = √a × √b (Multiplication Rule)
√(a ÷ b) = √a ÷ √b (Division Rule)
Only like radicals (same radicand) can be added/subtracted
k√a + m√a = (k + m)√a
k√a - m√a = (k - m)√a
√(a²) = a (for a ≥ 0)
Use FOIL method for binomial multiplication: (a±b)(c±d) = ac ± ad ± bc + bd
To divide binomials with radicals: Multiply numerator and denominator by the conjugate
Conjugate of (a + b√c) is (a - b√c)
(a + b√c)(a - b√c) = a² - b²c (Difference of squares)
√a × √a = a