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

If the radius of a circle is 7 cm, what is its circumference?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the greatest common divisor (GCD) of 36 and 48?

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What is the length of the diagonal of a square with a side length of 7 cm?

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If x^2 - 5x + 6 = 0, what are the roots?

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A man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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What is the sum of the first 50 positive integers?

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What is the remainder when 5^100 is divided by 3?

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If two complementary angles differ by 30°, what are the angles?

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What is the HCF of 48 and 180?

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