Math Problem Statement

Simplify the expression: sqrt((99^2 + 99) / 99)

Solution

The given mathematical expression is:

992+9999\sqrt{\frac{99^2 + 99}{99}}

Step-by-Step Solution:

  1. Simplify the expression inside the square root:

    992=980199^2 = 9801 Now substitute this into the expression:

    992+9999=9801+9999=990099\frac{99^2 + 99}{99} = \frac{9801 + 99}{99} = \frac{9900}{99}

  2. Simplify the fraction:

    990099=100\frac{9900}{99} = 100

  3. Apply the square root:

    100=10\sqrt{100} = 10

Final Answer:

1010

Would you like further clarification on any part of this solution?

Related Questions:

  1. How do you simplify expressions with square roots?
  2. What are some shortcuts for squaring numbers like 99?
  3. How do you factor numbers quickly to simplify expressions like this one?
  4. Can this expression be solved using algebraic identities?
  5. How would you approach this problem if 99 were replaced by another number?

Tip:

When simplifying square root expressions, always simplify the inside as much as possible before applying the square root.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Simplifying Radicals
Quadratic Numbers
Fractions

Formulas

a^2 = a * a
Simplifying fractions: (a^2 + a) / a = a + 1
Square root formula: sqrt(x)

Theorems

Basic properties of square roots and exponents

Suitable Grade Level

Grades 8-10