Question

a number squared increased by 5, is 41.

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the sentence into an equation

"A number squared" is \( x^2 \), "increased by 5" means \( x^2 + 5 \), and "is 41" gives the equation \( x^2 + 5 = 41 \).

Step3: Solve the equation for \( x \)

Subtract 5 from both sides: \( x^2 = 41 - 5 = 36 \).
Take the square root of both sides: \( x = \pm\sqrt{36} = \pm 6 \).

Answer:

The number is \( \pm 6 \)