This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to simplify the expression without a calculator: Step 1: Factor out the common term in the numerator. The common factor in 5^36 + 5^34 is 5^34. 5^36 + 5^34 = 5^34 · 5^2 + 5^34 · 1 = 5^34(5^2 + 1) Step 2: Simplify the term inside the parenthesis. 5^2 + 1 = 25 + 1 = 26 Step 3: Substitute this back into the expression under the square root. The expression becomes: 11 sqrt(5^34)(26)130 Step 4: Simplify the fraction inside the square root. Notice that 130 = 5 × 26. (26)/(130) = (26)/(5 × 26) = (1)/(5) Step 5: Rewrite the expression under the square root using the simplified fraction. 5^345 = 5^34-1 = 5^33 So the expression is now: 11 sqrt(5^33) Step 6: Simplify the square root of 5^33. We can write 5^33 as 5^32 · 5^1. sqrt(5^33) = sqrt(5^32) · 5 = sqrt(5^32) · sqrt(5) Since sqrt(5^32) = (5^32)^1/2 = 5^32/2 = 5^16. So, sqrt(5^33) = 5^16 sqrt(5). Step 7: Combine with the leading factor of 11. 11 · 5^16 sqrt(5) The simplified expression is 11 · 5^16 sqrt(5). Last free one today — make it count tomorrow, or type /upgrade for unlimited.