What is a square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √9 = 3 because 3² = 9.

What is the rule for multiplying square roots?

To multiply square roots, multiply the values inside the square roots and then find the square root of the result. For example, √2 * √8 = √(2*8) = √16 = 4.

What is a tip for simplifying square roots?

To simplify square roots, find the prime factors of the number inside the square root and look for pairs of factors. For example, √18 = √(9*2) = 3√2.

Solve for x: √x = 5. Hint: Square both sides to eliminate the square root.

Square both sides: (√x)² = 5², which simplifies to x = 25.

Solve the equation: √(x + 3) = 7. Hint: Start by squaring both sides to remove the square root.

Square both sides: (√(x + 3))² = 7², which simplifies to x + 3 = 49. Subtract 3 from both sides: x = 46.

What is the property of square roots regarding negatives?

The square root of a non-negative number is always non-negative. For example, √4 = 2, but √(-4) is not a real number.

If √a = 6, what is the value of a?

Square both sides: (√a)² = 6², which simplifies to a = 36.

What is the rule for adding square roots?

You can only add square roots directly if the values inside the square roots are the same. For example, √3 + √3 = 2√3, but √2 + √3 cannot be simplified further.

Find the value of x: √(2x) = 10. Hint: Begin by squaring both sides.

Square both sides: (√(2x))² = 10², which simplifies to 2x = 100. Divide both sides by 2: x = 50.

How do you simplify √(50)?

To simplify √(50), find its prime factors: 50 = 25 * 2. Thus, √(50) = √(25*2) = 5√2.