square root of 528
Understand the Problem
The question is asking for the square root of the number 528. To solve this, we will determine the value which, when multiplied by itself, equals 528.
Answer
The square root of 528 is approximately $22.976$.
Answer for screen readers
The square root of 528 is approximately $22.976$.
Steps to Solve

Identify the square root operation We need to find a number $x$ such that $x^2 = 528$. This means we are looking for $x = \sqrt{528}$.

Use a calculator or simplify the expression To find the value of $x$, we can either use a calculator or simplify the number first, if possible. First, we can break down 528 into its prime factors to ease the square root calculation.

Factor 528 Start with division:
 $528$ is even, divide by $2$: $528 \div 2 = 264$
 $264$ is even, divide by $2$: $264 \div 2 = 132$
 $132$ is even, divide by $2$: $132 \div 2 = 66$
 $66$ is even, divide by $2$: $66 \div 2 = 33$
 $33$ is divisible by $3$: $33 \div 3 = 11$
Thus, the prime factorization of 528 is: $$ 528 = 2^4 \times 3^1 \times 11^1 $$
 Calculate the square root using properties of exponents Using the prime factorization result, we can take the square root:
 For $2^4$: The square root is $2^{4/2} = 2^2 = 4$.
 For $3^1$: The square root is $3^{1/2} = \sqrt{3}$.
 For $11^1$: The square root is $11^{1/2} = \sqrt{11}$.
Combine these: $$ \sqrt{528} = 4 \cdot \sqrt{3 \cdot 11} = 4 \cdot \sqrt{33} $$
 Use a calculator for a numerical answer Now we can calculate an approximate value using a calculator: $$ \sqrt{528} \approx 22.976 $$
The square root of 528 is approximately $22.976$.
More Information
The square root calculation helps in various applications, including geometry, physics, and statistics. Understanding square roots also enhances number sense and familiarity with radical expressions.
Tips
 Confusing the operation of squaring with square roots. Remember that squaring a number means multiplying it by itself, while square roots find the length of one side of a square area.
 Not simplifying the radicals correctly or overlooking factors. Always break down the number into prime factors for easier calculations.