Questions: Simplify each expression. Assume that the variables represent any real numbers. Use the absolute value button only when necessary. (a) sqrt(y^6) = y^3 (b) sqrt(212) = .

Simplify each expression.
Assume that the variables represent any real numbers. Use the absolute value button only when necessary.
(a) sqrt(y^6) = y^3
(b) sqrt(212) = .

Transcript text: Simplify each expression. Assume that the variables represent any real numbers. Use the absolute value button only when necessary. (a) $\sqrt{y^{6}}=\mid y^{3}$ (b) $\sqrt{212}=\dot{\square}$

Solution

Solution Steps

To simplify the given expressions, we need to apply the properties of square roots and exponents.

(a) For $\sqrt{y^6}$, we can use the property that $\sqrt{a^2} = |a|$. Therefore, $\sqrt{y^6} = |y^3|$.

(b) For $\sqrt{212}$, we can find the square root using Python's math library.

Step 1: Simplify $\sqrt{y^6}$

To simplify $\sqrt{y^6}$, we use the property of square roots and exponents: $\sqrt{a^2} = |a|$. Therefore, $\sqrt{y^6} = |y^3|$.

Given $y = 2$: \[ \sqrt{2^6} = |2^3| = |8| = 8 \]

Step 2: Calculate $\sqrt{212}$

To find the square root of 212, we use the square root function: \[ \sqrt{212} \approx 14.56 \]

Final Answer

(a) $\sqrt{y^6} = |y^3|$ for $y = 2$: \[ \boxed{8} \]

(b) $\sqrt{212}$: \[ \boxed{14.56} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!