Square Roots of Primes

Square Roots of Primes

From Square Root of Prime is Irrational, no prime number can be expressed precisely by a rational fraction.

The decimal expansions of the square roots of some of the first few primes are as follows:

Square Root of $2$

$\sqrt 2 \approx 1 \cdotp 41421 \, 35623 \, 73095 \, 04880 \, 16887 \, 24209 \, 69807 \, 85697 \ldots$

Square Root of $3$

$\sqrt 3 \approx 1 \cdotp 73205 \, 08075 \, 68877 \, 2935 \ldots$

Square Root of $5$

$\sqrt 5 \approx 2 \cdotp 23606 \, 79774 \, 99789 \, 6964 \ldots$

Square Root of $7$

$\sqrt 7 \approx 2 \cdotp 64575 \, 13110 \, 64590 \, 5905 \ldots$

Square Root of $11$

$\sqrt {11} \approx 3 \cdotp 31662 \, 47903 \, 55399 \, 8491 \ldots$

Square Root of $13$

$\sqrt {13} \approx 3 \cdotp 60555 \, 12754 \, 63989 \, 2931 \ldots$

Square Root of $17$

$\sqrt 17 \approx 4 \cdotp 12310 \, 56256 \, 17660 \, 5498 \ldots$

Square Root of $19$

$\sqrt {19} \approx 4 \cdotp 35889 \, 89435 \, 40673 \, 5522 \ldots$

Square Root of $23$

$\sqrt {23} \approx 4 \cdotp 79583 \, 15233 \, 12719 \, 5415 \ldots$

Square Root of $29$

$\sqrt {29} \approx 5 \cdotp 38516 \, 48071 \, 34504 \, 0312 \ldots$

Square Root of $31$

$\sqrt {31} \approx 5 \cdotp 56776 \, 43628 \, 30021 \, 9221 \ldots$

Square Root of $37$

$\sqrt {37} \approx 6 \cdotp 08276 \, 25302 \, 92819 \, 6889 \ldots$

Square Root of $41$

$\sqrt {41} \approx 6 \cdotp 40312 \, 42374 \, 32848 \, 6864 \ldots$

Square Root of $43$

$\sqrt {43} \approx 6 \cdotp 55743 \, 85243 \, 02000 \, 6523 \ldots$

Square Root of $47$

$\sqrt {47} \approx 6 \cdotp 85565 \, 46004 \, 01044 \, 1249 \ldots$

Square Root of $53$

$\sqrt {53} \approx 7 \cdotp 28010 \, 98892 \, 80518 \, 2710 \ldots$

Square Root of $59$

$\sqrt {59} \approx 7 \cdotp 68114 \, 57478 \, 68608 \, 1757 \ldots$

Square Root of $61$

$\sqrt {61} \approx 7 \cdotp 81024 \, 96759 \, 06654\, 3941 \ldots$

Square Root of $67$

$\sqrt {67} \approx 8 \cdotp 18535 \, 27718 \, 72449 \, 9699 \ldots$

Square Root of $71$

$\sqrt {71} \approx 8 \cdotp 42614 \, 97731 \, 76358 \, 6306 \ldots$

Square Root of $73$

$\sqrt {73} \approx 8 \cdotp 54400 \, 37453 \, 17531 \, 1678 \ldots$

Square Root of $79$

$\sqrt {79} \approx 8 \cdotp 88819 \, 44173 \, 15588 \, 8500 \ldots$

Square Root of $83$

$\sqrt {83} \approx 9 \cdotp 11043 \, 35791 \, 44298 \, 8819 \ldots$

Square Root of $89$

$\sqrt {89} \approx 9 \cdotp 43398 \, 11320 \, 56603 \, 8113 \ldots$

Square Root of $97$

$\sqrt {97} \approx 9 \cdotp 84885 \, 78017 \, 96104 \, 7217 \ldots$