Question

(a) problem 10: which of these choices lists all of the square roots of the number 7? after you pick your answer press go. a. $sqrt{7}$ b. $sqrt{14}$, $-sqrt{14}$ c. $-sqrt{7}$ d. $+7$, $-7$ e. $sqrt{7}$, $-sqrt{7}$

Explanation:

Step1: Recall the definition of square roots

A square root of a number \( x \) is a value \( y \) such that \( y^2 = x \). For any positive real number \( a \), the square roots are \( \sqrt{a} \) and \( -\sqrt{a} \) because \( (\sqrt{a})^2 = a \) and \( (-\sqrt{a})^2 = a \).

Step2: Apply the definition to the number 7

For the number 7, we need to find all \( y \) such that \( y^2 = 7 \). Let's check each option:

• Option A: Only \( \sqrt{7} \), but we also need \( -\sqrt{7} \) since \( (-\sqrt{7})^2 = 7 \), so A is incorrect.
• Option B: \( \sqrt{14} \) and \( -\sqrt{14} \), but \( (\sqrt{14})^2 = 14

eq 7 \), so B is incorrect.

• Option C: Only \( -\sqrt{7} \), missing \( \sqrt{7} \), so C is incorrect.
• Option D: \( +7 \) and \( -7 \), but \( 7^2 = 49

eq 7 \), so D is incorrect.

• Option E: \( \sqrt{7} \) and \( -\sqrt{7} \), since \( (\sqrt{7})^2 = 7 \) and \( (-\sqrt{7})^2 = 7 \), this lists all square roots of 7.

Answer:

E. \( \sqrt{7}, -\sqrt{7} \)