Topic 1: Square root of a rational perfect square
Problem 1: Find the square root of 16/25. Simplify the fraction and compute the result.
Problem 2: Compute the square root of 81/4. Simplify and provide the exact value.
Topic 2: Pythagorean Theorem
Problem 1: In a right triangle with legs of 6 cm and 8 cm, use the Pythagorean Theorem to find the hypotenuse.
Problem 2: A right triangle has legs of 9 m and 12 m. Apply the Pythagorean Theorem to calculate the hypotenuse.
Topic 3: Word problem involving the Pythagorean Theorem
Problem 1: A ladder is 15 ft long and reaches 12 ft up a wall. Use the Pythagorean Theorem to find the distance from the base of the ladder to the wall.
Problem 2: A rectangle has a diagonal of 17 cm and a width of 8 cm. Find the length using the Pythagorean Theorem.
Topic 4: Finding all square roots of a number
Problem 1: Find all square roots of 25. List both the positive and negative roots.
Problem 2: Determine all square roots of 100. Provide both the positive and negative values.
Topic 5: Square roots of perfect squares with signs
Problem 1: Evaluate ±√49. Provide both square roots and explain the signs.
Topic 6: Square roots of integers raised to even exponents
Problem 1: Simplify √(5^4). Express the result as a single number.
Topic 7: Introduction to simplifying a radical expression with an even exponent
Problem 1: Simplify √(x^4). Explain the process and write the simplified expression.
Problem 2: Simplify √(y^26). Show the steps and provide the result.
Topic 8: Square root of a perfect square monomial
Problem 1: Simplify √(16x^2). Factor the expression and compute the square root.
Problem 2: Compute √(25y^4). Simplify the monomial under the square root.
Topic 9: Simplifying the square root of a whole number less than 100
Problem 1: Simplify √18. Identify if it’s a perfect square and provide the result.
Topic 10: Simplifying the square root of a whole number greater than 100
Problem 1: Simplify √120. Verify it’s a perfect square and provide the result.
Topic 11: Simplifying a radical expression with an even exponent
Topic 12: Introduction to simplifying a radical expression with an odd exponent
Problem 1: Simplify √(x^5). Break down the exponent and express the result.
Topic 13: Simplifying a radical expression with an odd exponent
Problem 1: Simplify √(8x^3). Factor and simplify the expression under the radical.
Topic 14: Simplifying a radical expression with two variables
Problem 1: Simplify √(40x^12y^11). Factor the expression and simplify the radical.
Problem 2: Compute √(25a^4b^2). Simplify the multivariate radical expression.
Topic 15: Introduction to square root addition or subtraction
Topic 16: Square root addition or subtraction
Topic 17: Square root addition or subtraction with three terms
Topic 18: Introduction to simplifying a sum or difference of radical expressions: Univariate
Topic 19: Simplifying a sum or difference of radical expressions: Univariate
Topic 20: Introduction to square root multiplication
Problem 1: Explain how to multiply √5 * √3. Compute the product and simplify.
Problem 2: Describe the process to multiply √7 * √2. Provide the simplified result.
Topic 21: Square root multiplication: Basic
Topic 22: Square root multiplication: Advanced
Topic 23: Introduction to simplifying a product of radical expressions: Univariate
Topic 24: Simplifying a product of radical expressions: Univariate
Topic 25: Simplifying a product of radical expressions: Multivariate
Topic 26: Introduction to simplifying a product involving square roots using the distributive property
Problem 1: Simplify √3 (√6 + √2). Use the distributive property and simplify the result.
Problem 2: Compute √5 (√10 - √20). Apply the distributive property and simplify.
Topic 27: Simplifying a quotient of square roots
Topic 28: Rationalizing a denominator: Quotient involving square roots
Problem 1: Rationalize the denominator of 5/√3. Multiply by the conjugate and simplify.
Problem 2: Simplify 7/√5 by rationalizing the denominator. Show the steps and result.
Topic 29: Rationalizing a denominator: Square root of a fraction
Problem 1: Rationalize the denominator of √7 / √2. Simplify the expression.
Problem 2: Compute √10 / √5 and rationalize the denominator. Provide the simplified form.
Topic 30: Rationalizing a denominator: Quotient involving a monomial
Problem 1: Rationalize the denominator of 3 / √(2x). Multiply by the conjugate and simplify.
Problem 2: Simplify 6 / √(3y^2). Rationalize the denominator and express the result.