Topic Details (Notes format)

How to Solve Radical Equations (Equations with Square Roots)

Subject: Mathematics

Book: Maths Mastery

Radical equations contain variables under a radical (e.g., √(x+1)=x–3). Generally, isolate the radical, then square both sides carefully. For instance, √(x+1)=x–3 implies x+1=(x–3)²= x²–6x+9, giving x²–7x+8=0. Solutions must be checked to exclude extraneous ones introduced by squaring. This approach appears in geometry (distance formulas), physics (velocity or acceleration equations), and advanced algebra. Consistent practice ensures you systematically remove radicals, preserving correct solutions without false inclusions.

Practice Questions

A number is increased by 20% and then decreased by 20%. What is the net change?

View Question

If sin(A) = 3/5 and cos(B) = 5/13, where A and B are acute angles, what is sin(A+B)?

View Question

If the probability of an event is 1/4, what is the probability of its complement?

View Question

What is the square root of 0.25?

View Question

If x = 2 and y = 3, what is the value of (x^2 + y^2)?

View Question

If a cone has a base radius of 3 cm and height of 4 cm, what is its slant height?

View Question

If 2a + b = 10 and a - b = 4, what is the value of a?

View Question

If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

View Question

If the average of five consecutive odd numbers is 25, what is the largest number?

View Question

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

View Question