[tex]5 \sqrt{540} [/tex]fine the quotient​

Step-by-step explanation:Step 1: Factor out perfect squares from the radicand The radicand is the number under the radical sign. In this case, the radicand is 540. We need to find the largest perfect square that divides 540. - 540 is divisible by 4, which is a perfect square.- 540/4 = 135- 135 is divisible by 9, which is also a perfect square.- 135/9 = 15 Therefore, we can rewrite 540 as:[tex] 540= 4 \times 9 \times 15 = 2^2 \times 3^2 \times 15 [/tex] Step 2: Simplify the radical Now we can rewrite the original expression as: [tex] 5\sqrt{540} = 5\sqrt{2^2 \times 3^2 \times 15} [/tex] Using the property of radicals that states [tex]\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}[/tex], we can simplify: [tex] 5\sqrt{2^2 \times 3^2 \times 15} = 5 \times \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{15} [/tex] Since the square root of a squared number is the number itself, we get: [tex] 5 \times \sqrt{2^2} \times \sqrt{3^2} \times \sqrt{15} = 5 \times 2 \times 3 \times \sqrt{15} = 30\sqrt{15}[/tex] Answer Therefore, the simplified form of [tex] 5\sqrt{540} [/tex] is [tex] 30\sqrt{15} [/tex].

Answered by paredesprancheskapet | 2024-10-21