Simplifying Square Roots
This Grade 6 algebra skill from Yoshiwara Elementary Algebra teaches students to simplify square root expressions by extracting perfect square factors. Students identify the largest perfect square factor of the radicand and apply the product rule for radicals to write the expression in simplified form.
Key Concepts
Property To Simplify a Square Root: 1. Factor any perfect squares from the radicand. 2. Use the product rule to write the radical as a product of two square roots. 3. Simplify the square root of the perfect square.
Examples To simplify $\sqrt{50}$, we find the perfect square factor 25. So, $\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25}\sqrt{2} = 5\sqrt{2}$. To simplify $\sqrt{72}$, we use the largest perfect square factor, 36. So, $\sqrt{72} = \sqrt{36 \cdot 2} = \sqrt{36}\sqrt{2} = 6\sqrt{2}$. To simplify $\sqrt{108}$, we factor it as $\sqrt{36 \cdot 3}$. This simplifies to $\sqrt{36}\sqrt{3} = 6\sqrt{3}$.
Explanation Simplifying a radical means pulling out any perfect square factors hiding inside the radicand. Find the largest perfect square that divides your number, separate it, and take its root, leaving the rest inside.
Common Questions
How do you simplify a square root?
Find the largest perfect square factor, then separate it using the product rule. For example, sqrt(48) = sqrt(16 x 3) = 4sqrt(3).
What is a perfect square?
A perfect square is the square of an integer, such as 1, 4, 9, 16, 25, 36. Their square roots are whole numbers.
When is a square root in simplified form?
A square root is simplified when the radicand has no perfect square factors other than 1.
How do you simplify sqrt(72)?
Factor: 72 = 36 x 2. So sqrt(72) = sqrt(36) x sqrt(2) = 6sqrt(2).
Where is simplifying square roots taught in Grade 6?
Simplifying square roots is covered in the Yoshiwara Elementary Algebra textbook for Grade 6.