Question:
prove that 7/5 √5 is an irrational number
Answer:
Let I = 7/(5 + √5)
After rationalizing, we get
=> I = {7 * (5 - √5)}/{(5 + √5)*(5 - √5)}
=> I = {7 * (5 - √5)}/{(5)2 - (√5)2 }
=> I = {7 * (5 - √5)}/(25 - 5)
=> I = {7 * (5 - √5)}/20
Now, we know that √5 is an irrational number.
So, {7 * (5 - √5)}/20 is also an irrational number.
Hence, 7/(5 + √5) is an irrational number.
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