Question

find the value of 1by root2​

Answer 1

Answer:

please check the image above

Answer 2

The value of 1/√2 is √2/2. This can be found by rationalizing the denominator or using the trigonometric values of a 45-degree angle. Alternatively, we can use a calculator to get an approximate decimal value.

To find:

• The value of 1/√2

Given:

• 1/√2

Solution:

To find the value of 1/√2, we can use a few different methods:

Method 1: Rationalizing the denominator:

• We can start by rationalizing the denominator of 1/√2 to get √2/2. To do this, we multiply both the numerator and denominator of 1/√2 by √2:
• 1/√2 x √2/√2 = √2/2
• Therefore, the value of 1/√2 is √2/2.

Method 2: Using trigonometric values:

• Another way to find the value of 1/√2 is to use the trigonometric values of a 45-degree angle in a right-angled triangle. In a 45-45-90 triangle, the two smaller sides are equal in length and the hypotenuse is √2 times the length of the smaller sides. If we let one of the smaller sides be 1, then the other smaller side is also 1 and the hypotenuse is √2. Therefore, the sine and cosine of 45 degrees are both 1/√2:
• sin 45° = 1/√2
• cos 45° = 1/√2

Method 3: Using the decimal approximation:

• We can also use a calculator or math software to find an approximate value of 1/√2. Using a calculator, we get:
• 1/√2 = 0.7071067811865475 (rounded to 16 decimal places)

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