Flashcards on Surds

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What is a surd?

A surd is an irrational number in the form of √n, where n is a non-perfect square.

State a property of surds.

One property of surds is that the sum (or difference) of two surds of the same order is a surd.

How can surds be simplified?

Surds can be simplified by finding the largest perfect square factor of the radicand and taking its square root out of the square root sign.

What is the result of √8 - √2 + √18?

The result is 2√2 + √2√2 + 3√2 = 6√2.

How do you rationalize the denominator of a fraction with a surd?

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator.

Solve the equation √(2x+3) = 5.

Squaring both sides, we get 2x + 3 = 25. Solving for x, we find x = 11.

What are some real-life applications of surds?

Surds are used in various fields such as engineering, physics, and computer science to solve problems involving measurement, calculations, and modeling.

How are surds related to geometry?

Surds are often used to represent lengths or side ratios in geometric figures, such as the diagonal of a square or the hypotenuse of a right triangle.

Define a surd in terms of its components.

A surd consists of a radicand, which is the number under the square root sign, and the surd symbol, which indicates that the number is irrational.

What is the product of two surds √a and √b?

The product is √(ab).

Simplify √(16/25).

The simplified form is 4/5.

What is the result of (√2 + √3)^2?

Expanding the square, we get 2 + 2√6 + 3 = 5 + 2√6.

How do you add or subtract surds?

To add or subtract surds, combine like terms by adding or subtracting the coefficients in front of the surd symbols.

Solve the equation √(x+1) + √(x-1) = 4.

By squaring both sides and solving the resulting quadratic equation, we find x = 7.

What is the result of √3 + √3 + √3?

The result is 3√3.

What is a surd?

A surd is an irrational number in the form of √n, where n is a non-perfect square.

State a property of surds.

One property of surds is that the sum (or difference) of two surds of the same order is a surd.

How can surds be simplified?

Surds can be simplified by finding the largest perfect square factor of the radicand and taking its square root out of the square root sign.

What is the result of √8 - √2 + √18?

The result is 2√2 + √2√2 + 3√2 = 6√2.

How do you rationalize the denominator of a fraction with a surd?

To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator.

Solve the equation √(2x+3) = 5.

Squaring both sides, we get 2x + 3 = 25. Solving for x, we find x = 11.

What are some real-life applications of surds?

Surds are used in various fields such as engineering, physics, and computer science to solve problems involving measurement, calculations, and modeling.

How are surds related to geometry?

Surds are often used to represent lengths or side ratios in geometric figures, such as the diagonal of a square or the hypotenuse of a right triangle.

Define a surd in terms of its components.

A surd consists of a radicand, which is the number under the square root sign, and the surd symbol, which indicates that the number is irrational.

What is the product of two surds √a and √b?

The product is √(ab).

Simplify √(16/25).

The simplified form is 4/5.

What is the result of (√2 + √3)^2?

Expanding the square, we get 2 + 2√6 + 3 = 5 + 2√6.

How do you add or subtract surds?

To add or subtract surds, combine like terms by adding or subtracting the coefficients in front of the surd symbols.

Solve the equation √(x+1) + √(x-1) = 4.

By squaring both sides and solving the resulting quadratic equation, we find x = 7.

What is the result of √3 + √3 + √3?

The result is 3√3.

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