(3√3) square -(2√2) square
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Answers
Answer:
Step-by-step explanation:
Answer:
19
Step-by-step explanation:
Given: (3√3)² - (2√2)² we need to find out it's value. Root can be written as ½ as meaning is same.
Therefore,
→ (3 × 3^½)² - (2 × 2^½)²
→ (3)² × (3)²*½ - (2)² × (2)²*½
This symbol ( * ) means multiply. Whereas 2*½ means 2/2. On solving powers we get,
→ 9 × 3 - 4 × 2
→ 27 - 8
→ 19
IN SHORT:
→ (3√3)² - (2√2)²
→ 9(3) - 4(2)
→ 27 - 8
→ 19
Therefore, the value of (3√3)² - (2√2)² is 19.
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Let's take more examples to solve such type of questions.
1) 4 - 2(√2)². In this square is only on √2 and we already know that root means ½, so on solving power we get 2.
→ 4 - 2(2)
→ 4 - 4
→ 0
Value of 4 - 2(√2)² is 0.
2) (√5 + √3)/(√5 - √3) such type of questions are solved by rationalisig the denominator (whenever we do rationalise, we use opposite sign, that of the given sign in denominator).
→ (√5 + √3)/(√5 - √3) × (√5 + √3)/(√5 + √3)
→ [√5(√5 + √3) + √3(√5 + √3)]/[(√5 - √3)(√5 + √3)]
Used identity: (a + b) (a - b) = a² - b²
→ (5 + √15 + √15 + 3)/(5 - 3)
→ (8 + 2√15)/2
→ 4 + √15