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Vitek1552 [10]
3 years ago
5

Find the square root of 14+6√5​

Mathematics
1 answer:
Novosadov [1.4K]3 years ago
6 0

<u>Answer:</u>

3 + √5

<u>Step-by-step explanation:</u>

Find the square root of 14+6√5​

Change to √ ( 14 + 6√5 ) = √x + √y

1️⃣ Square.

<em>14 + 6√5 = x + y + 2√xy</em>

<em>14 + 2√45 = ( x + y) + 2√xy</em>

2️⃣ Compare.

<em>(x + y) = 14</em>

<em>xy = 45</em>

3️⃣ Solve.

<em>(x - y)² = (x+y)² - 4xy</em>

<em>( x - y)² = 14² - 180</em>

<em>( x - y)² = 196 - 180</em>

<em>( x - y)² = 16</em>

<em>( x - y) = 4</em>

<em />

<em>x + y = 14</em>

<em>x - y = 4</em>

<em />

<em>2x = 18</em>

<em>x = 9 .</em>

<em />

<em>y = 5 .</em>

<em />

<em>14 + 6√5 = √9 + √5 = 3 + √5 .</em>

Answer: 3 + √5 .

Done ✔

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