Question

qr = \sqrt{(4 + 2)^2 + (9 + 5)^2}

Explanation:

Step1: Simplify the expressions inside the square root

First, calculate the values inside the parentheses: \(4 + 2 = 6\) and \(9 + 5 = 14\). So the expression becomes \(\sqrt{6^{2}+14^{2}}\).

Step2: Calculate the squares

Next, find the squares of 6 and 14: \(6^{2}=36\) and \(14^{2} = 196\). Now the expression is \(\sqrt{36 + 196}\).

Step3: Add the numbers inside the square root

Add 36 and 196: \(36+196 = 232\). So we have \(\sqrt{232}\).

Step4: Simplify the square root (optional, but to get a simplified radical form or decimal)

We can factor 232: \(232=4\times58\), so \(\sqrt{232}=\sqrt{4\times58}=2\sqrt{58}\approx15.23\) (if we want the decimal approximation).

Answer:

If we want the simplified radical form, the answer is \(2\sqrt{58}\); if we want the decimal approximation, the answer is approximately \(15.23\). (Or following the original expression's calculation steps, the final value after computing \(\sqrt{(4 + 2)^{2}+(9 + 5)^{2}}=\sqrt{6^{2}+14^{2}}=\sqrt{36 + 196}=\sqrt{232}\approx15.23\) or \(2\sqrt{58}\))